If you believe that Messiah Jesus is a human being what logic you have to guess that he could be a God or son of God?

God is the source of all and is love, Christ is the perfect example of love within a broken world. Christ was begotten not made for He proceeded from the source (God) through a righteous and pure womb (Mary) into an unrighteous world. He is the light of love to the world that proceeded from the source. God spoke let their be light as the Spirit of God hovered over the waters of creation, thus, God became manifest in physical form in the world as the light of love that is the foundation of all within creation. This is a parallel to the first creation story. When we look into a mirror we see our mother and our father. Therefore, when we look at Christ, we see a suffering Creation and also a loving God - the foundation of both. Jesus is both Son of God (love) and Son of Man (judgement). A mystery for you to ponder with the help of Christ.

In the bible Jesus is revealed as the Word of God in many places. As Nigel J has pointed out, apart from the Divine self-revelation of Scripture we would all be just making stuff up. So logic and reason can be applied to Scripture but Scripture must come first.

In the beginning was the Word, and the Word was with God, and the Word was God.  He was in the beginning with God. - John 1:1-2

That which was from the beginning, which we have heard, which we have seen with our eyes, which we looked upon and have touched with our hands, concerning the word of life— the life was made manifest, and we have seen it, and testify to it and proclaim to you the eternal life, which was with the Father and was made manifest to us—  that which we have seen and heard we proclaim also to you, so that you too may have fellowship with us; and indeed our fellowship is with the Father and with his Son Jesus Christ. - 1 John 1:1-3

Then I saw heaven opened, and behold, a white horse! The one sitting on it is called Faithful and True, and in righteousness he judges and makes war.  Rev His eyes are like a flame of fire, and on his head are many diadems, and he has a name written that no one knows but himself. He is clothed in a robe dipped in blood, and the name by which he is called is The Word of God. - Revelation 19:11-13

The concept of God's Word is that it is not just the expression of the Word (as in speaking) but also the thought behind and preceding the Word (as in reasoning). Therefore, unless God can be imagined without mental activity, the Word has always existed as the Divine Thought (refer to John 1:1 above). Since Almighty God is infinite and eternal, so is His mental activity and He never thinks anything that is not perfectly integrated with who He is. It is this aspect of Himself that was incarnated in a human body.

And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth. - John 1:14

The purpose of the incarnation was the redemption of Man and for God to reconcile all things unto Himself but I don't think that is part of your question. You seem to be asking, "How can this be that God has a human Son?"

The incarnation (the birth, life, and death of Jesus Christ) is not when He became God's Son. A son is begotten and is the same nature and essence as that by which the begetting came. A person has a human child, cows beget cows and God produces a divine child. The child 'goes forth' from the parent as a distinct entity yet with the same nature.

“For as the rain and the snow come down from heaven and do not return there but water the earth, making it bring forth and sprout, giving seed to the sower and bread to the eater, so shall my word be that goes out from my mouth; it shall not return to me empty, but it shall accomplish that which I purpose, and shall succeed in the thing for which I sent it. - Isaiah 55:10-11

That which God has begotten of His very nature, that which has gone forth from His essence, from the mind of God, is His Word: This Divine activity and expression is the Son of God. The Son (the Divine Thought) is as infinite and eternal as God Himself. The Son proceeds from God but is not different. God has perfect integrity and what He thinks and says is exactly the same as who He is.

It is this Son that became flesh in the womb of a virgin woman.

Have this mind among yourselves, which is yours in Christ Jesus,  who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men. And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross. Therefore God has highly exalted him and bestowed on him the name that is above every name, so that at the name of Jesus every knee should bow, in heaven and on earth and under the earth, and every tongue confess that Jesus Christ is Lord, to the glory of God the Father. - Philippians 2:5-11

The Son of God (Word of God) has always existed. He cannot exist without the Father because He comes from the Father. God the Father has always existed. He could exist without the Son (Word) since the Son (Word) comes from Him but, since God the Father has never been without mental activity, the Son of God (Word of God) has always been with Him and is himself God. That eternal Son was made into flesh and, having been sent by the Father for that expressed purpose of fulfilling the law as a man and redeeming mankind as a sacrifice, He emptied himself and humbled himself.

How can it be that Almighty God would love sinful man so much?

God demonstrates his own love for us in this; while we were still sinners, Christ died for us. - Romans 5:8

The question of whether there exists similarity between God and Man appears to be of some great concern to you. The story of creation in Genesis lays the foundation for all that follows.

In Genesis 1, on the sixth day of creation, we have this:

26 Then God said, “Let us make mankind in our image, in our likeness, 
so that they may rule over the fish in the sea and the birds in the sky, 
over the livestock and all the wild animals, and over all the creatures 
that move along the ground.”

27 So God created mankind in his own image,
    in the image of God he created them;
    male and female he created them.

The possibility of God taking on a human form is found in those verses. Because God made mankind in His image, such a form is capable of holding God's spirit and showing forth His glory undiminished.

Mankind (through Adam and Eve) sinned and marred the image of God inside them, but Jesus, through the Virgin birth when Mary (or Maryam) conceived by the Holy Spirit, has an unfallen human nature, which therefore has an unmarred image of God.

When the Prophet Job suffered, he not only cried out to God for a savior, he did something more. Chapter by chapter, Job created a Job description for a savior. He listed every quality such a savior must have, and the principle actions that such a savior must perform in order to rescue him from sin, sickness, mortality and his terror of God.

1. In Job 6:8-10, Job places his hope in the Word of God, as the Apostle John would later call Jesus in John 1. Jesus, the eternal, uncreated word of God.

2. In Job 9, Job declares that he needs someone powerful like God to save him, but also someone like a man who can sympathize with him and not terrify him. There are four verses in this chapter that point to Jesus walking on water, a sign of divinity. This points to the incarnation, when God comes forth as both God and man in the form of Jesus.

3. In Job 13:15-16, "though he slay me, I will hope in him", corresponds to baptism, in which we are buried with Christ so that we may rise with him. At baptism, Jesus was annointed as savior, and here Job declares his hope in a savior.

4. In Job 14:13-17, he speaks of his renewal, his healing and forgiveness. The core of Jesus' ministry was healing people as a sign of their forgiveness from sins.

5. In Job 17:3-5; 33:22-26, you can see descriptions of the betrayal of Jesus at Gethsemane, such as "He who informs against his friends to get a share of their property" as a reference to Judas.

6. In Job 17:13-16; 33:27-39, 38:17, you have a detailed description of many events that occurred at the crucifixion of Jesus, such as people piercing him and him making a covenant.

7. In Job 19:23-27, you have Job's powerful testimony of faith:

   “Oh that my words were written! Oh that they were inscribed in a book! 24 Oh that with an iron pen and lead they were engraved in the rock forever! 25 For I know that my Redeemer lives, and at the last he will stand upon the earth. 26 And after my skin has been thus destroyed, yet in my flesh I shall see God, 27 whom I shall see for myself, and my eyes shall behold, and not another. My heart faints within me!

This speaks of the resurrection from the dead.

8. In Job 21:31, Job speaks extensively about the need for God to exercise judgment against the wicked. This corresponds to the Second Coming of Christ, when "he will come to judge the quick and the dead".

9. In Job 23:10-14, Job speaks of how he will be perfected, made like pure gold.

   But he knows the way that I take; when he has tried me, I shall come out as gold. 11 My foot has held fast to his steps; I have kept his way and have not turned aside. 12 I have not departed from the commandment of his lips; I have treasured the words of his mouth more than my portion of food. 13 But he is unchangeable, and who can turn him back? What he desires, that he does. 14 For he will complete what he appoints for me, and many such things are in his mind.

All Christians believe that when Jesus returns, we will be changed and made perfect.

So Job describes what he needs in a savior, his job description. What does God say to this?

7 After the Lord had spoken these words to Job, the Lord said to Eliphaz the Temanite: “My anger burns against you and against your two friends, for you have not spoken of me what is right, as my servant Job has. 8 Now therefore take seven bulls and seven rams and go to my servant Job and offer up a burnt offering for yourselves. And my servant Job shall pray for you, for I will accept his prayer not to deal with you according to your folly. For you have not spoken of me what is right, as my servant Job has.” 9 So Eliphaz the Temanite and Bildad the Shuhite and Zophar the Naamathite went and did what the Lord had told them, and the Lord accepted Job's prayer.

God agreed with Job's request, agreed that what Job needed from God was correct.

The three friends said many wrong things, but here is the place where Bildad sums up their entire argument:

“Dominion and fear are with God;
    he makes peace in his high heaven.
3 Is there any number to his armies?
    Upon whom does his light not arise?
4 How then can man be in the right before God?
    How can he who is born of woman be pure?
5 Behold, even the moon is not bright,
    and the stars are not pure in his eyes;
6 how much less man, who is a maggot,
    and the son of man, who is a worm!”

The last line is the kicker: Bildad ridicules Job for trusting in "the son of man". He denies that a man "born of woman" can save anyone. Bildad denies that God can become a man.

And God said that Bildad was wrong.

This speech of God to Job is unique. It is God's longest speech in the Bible to any person. At the end, God grants Job the authority to pronounce forgiveness on his friends, unprecedented in history.

Above I gave nine instances where Job either declared what he needed in a savior or described prophetically the actions to be taken by such a savior. This is where it gets interesting. Those nine instances point to nine events in the life and ministry of Christ. They were prophesied 1,700 yers before Jesus was born. AND THEY WERE SPOKEN BY JOB IN CHRONOLOGICAL ORDER! The odds of that happening by chance are 9! to one. That is nine factorial to one, or one chance in 362,880.

To sum up:

1. In creation, God made humans in His image, meaning that the image of a human is capable of representing God if he chooses.
2. Job listed the essential characteristics and actions of a savior.
3. Those characteristics match Jesus and no one else in history.
4. God endorsed Job's statements.
5. God condemned the friend's statements, including the idea that the savior could not be a "son of man".
6. Jesus was born and fulfilled all of Job's prophecies, as well as the prophecies of many prophets since then.

My argument has been brief. For a more detailed exegesis of the verses I have cited to back my argument, see my book Job Rises: Thirteen Keys to a Resilient Life.

It is very simple. The Christian God and the Islamic God/Allah [not sure what term to use there; sorry] are very different.

(Arguably, they can not both be right. Thus, one of them is wrong [or both]. It is no surprise that the right religion and a wrong religion are very different, regardless of which is which. (It would be interesting to argue over the history, since they [claim to] have the same roots, but that is not my area. Also off-topic.) )

One of the fundamental points about the incarnation [God becoming a human being] is precisely as the OP discusses — to show us what God is like — or what he would be like if he were a human being, if you prefer.

Gen 1: 27  “So God created man in his own image, in the image of God he created him; male and female he created them.”
John 14: 9  “Jesus said to him, “Have I been with you so long, and you still do not know me, Philip?  Whoever has seen me has seen the Father. How can you say, ‘Show us the Father’?”

As the OP says so well, Jesus had a human birth, lived a human life, worked, went to the toilet, suffered pain, wept, fled for his life [that is, his parents did], got exasperated, suffered persecution from political authorities, ate food, got tired… the whole nine yards — the real thing.

(He also raised people from the dead, cured sickness, stilled storms, cast out demons… .  He was also inordinately good at both refuting his opponents and shaming them, all with literally about 10 or 15 words.)

It gets much more extreme. The Christian picture is that God  • took sin [evil] upon himself (at least metaphorically) and  • died an excruciating death  particularly to reconcile to himself persons who were still evil… and now dwells within them, still while they are evil. …That he chose to do this, when he did not have to, because he loves them.

As the OP says, there is absolutely no possibility that this is Allah.

Christian don't claim that Jesus became God, or that God became man; that is, at least, in the sense that one nature becomes the other nature (the eternal cannot become not-eternal, nor can the temporal become eternal).

Rather, we believe that the eternal, personal Word or Son or Wisdom of God became flesh in order to dwell among us - He's no less capable of using flesh for His tabernacle than He is of using a stone Temple for such.

The reason Jesus is God is that His person is the Word of God. His person didn't originate in Mary's womb, or originate at all. Rather, Mary concieved the Word of God as He became flesh. The Word living in flesh was the novelty - not the Divine Person Himself, He always existed.

This is that we can worship Him, because He is eternal and God, but also why He can suffer - He took flesh for Himself to live in.

Christians agree with Muslims (I'm assuming you're Muslim) that God is not a man, nor that the Divine Nature can become a man. Everything in existence would cease to exist. But that God could take a human nature, not for some created personality, but for Himself, that isn't even difficult to believe, let alone impossible.

Jesus is not a What but a Who.

The Bible teaches that there is only one God, period. The Bible also teaches that God is spirit, or a spiritual being by nature/essence. (John 4:24).

The Bible also teaches that "ALL" men are sinners, without exception human being are sinners, period. (Romans 3:23) In addition, Romans 6:23 says, "For the wages/payment for sinning is death, but the free gift of God is eternal life in Christ Jesus our Lord."

There are two deaths for man, one is physical death and the other is spiritual death. Spiritual death is separation from God for all eternity. The verse I just quoted says we do not have to be separated from God in spiritual death because God offers us the free gift of eternal life in Jesus Christ His Son.

Remember mr. rafik I stated God is a spiritual being who cannot be seen with the physical eyes. His Son Jesus Christ said, "Not that any man hath see the Father, except he who is from God, he hath seen the Father." (John 6:46). And John 1:18, "No man has seen God/the Father at anytime, the only begotten Son, who is in the bosom of the Father, He has EXPLAINED Him.

To see the Son is to see the Father because the Son is the only physical manifestation of the Son. So what about the Son? Where did He come from? According to John 1:1-14 the Son eternally existed with the Father. Then at the appointed time, "But when the fulness of the time came. God sent forth His Son, born of a woman under the Law, (why?) in order that He might redeem those who were under the Law that we might receive the adoption as sons." (Galatians 4:4-5).

As you said Jesus was born through Maryam a human being. The father of Jesus was not a "biological" father but as the Bible teaches God was His Father. Hebrews 1:5, "Thou art My Son, Today I have begotten Thee, and again, I WILL BE A FATHER TO HIM AND HE SHALL BE A SON TO ME."

So, Jesus Christ is the only person with two natures. One on His mother's side which is human being, and one on His Father's side which is deity. It's a universal law that a son shares the same nature as his father.

So here you have God the Son taking our place by dying on the cross so you and I can have spiritual life and forever be with the Lord God. All you have to do is put your trust in Jesus Christ. By the way, this is the "epitome" of love and does not decrease the greatness of God as you said, it increases the greatness of God and His love for all of us. Can you please tell me what Allah has to offer that's better than this?

No 'guess-work' is required or appropriate. The 'logic' necessary to understand the revelation of the true God is provided by God himself.

The Messiah promised in the Hebrew scriptures (Genesis to Malachi) was promised by prophetic revelation. That revelation was expressed divinely to chosen prophets and conveyed in scripture, a process of several thousand years.

It is abundantly clear that this revelation has been - fully - fulfilled in Jesus Christ of Nazareth, according to a multitude of scriptures too numerous to mention in a brief answer on a website. This fulfillment of revelation has been meticulously documented in the Greek scriptures, during the first century AD.

The revelation of the true Deity was a progressive revelation. That revelation was begun by Hebrew prophets - divinely chosen by the God of Abraham, Isaac and Jacob - and that expression of revelation was completed by the apostles chosen of Jesus Christ, as recorded in the Greek scriptures (Matthew to Revelation).

That revelation is truly astounding : 'God was manifest in flesh.' 'Jesus Christ is come in flesh.' 'Emmanuel' is 'God with us'.

What is revealed is that Another Humanity was always in the purpose of the eternal Deity, determined before the foundation of the world. That humanity is given of God himself, a new creation. And that humanity is manifested - in Headship - by God himself. This manifestation is the revelation of the Son of God, who - in turn - reveals the Father.

That humanity is other than that come under the headship of Adam. And this was promised to Adam himself whilst yet in the garden of Eden in the beginning.

This breathtaking revelation is made known only in the Hebrew and Greek scriptures, Genesis to Revelation. It is not documented, by Divine authorisation, anywhere else.

Any other documentation which contradicts this Divinely recorded revelation, must - by necessary logic - be false.

The Christian logic is that God (Allah) incarnated into a baby that was miraculously conceived within Maryam's womb without sexual intercourse, a doctrine called the Virgin Birth.

While being Jesus, God remains the Father simultaneously, so at no point in time God loses any of His divinity nor his greatness. Obviously it was God's will and His Divine power which made this possible.

Why did He do this? In order for God (Allah) to save humanity from original sin so all human beings who are willing to make Jesus our Lord and Savior will have eternal life

The logic is:

1. Only God can fully forgive sin
2. Only 100% human can be the representative to be in solidarity with humanity

Therefore Jesus has to be fully God and fully Human, a doctrine called the Hypostatic Union.

Addressing the objection:

By that answer you are decreased the greatness of God (Allah)

In the Christian logic (the doctrine of Trinity), God is still fully God, so there is no reduction of God's greatness by being human. Jesus as a man, prays to God the Father, who remains fully divine. It is not like when God incarnated into Jesus there was no God in charge anymore.

Allah never be similar with human being at all

In the Christian logic, God is the creator of all the universe, including human beings. Why is it that the Creator cannot assume a human body? God is Almighty and All powerful. Islam believes this too. It is the other way around that is not possible. No human can become God. Christians don't believe this is possible.

ADDENDUM

• For a much more precise "technical" description of the Incarnation please see the Catholic Catechism on this line from the Nicene Creed: "He was conceived by the power of the Holy Spirit, and born of the virgin Mary."

• Sola Gratia's answer is also very good.