If God set the maximum age to 120, then how could Jacob be 130 years old?

When God said man's days will be 120, he didn't mean he would not allow people to live longer if that suited his plan. Indeed he is offering us Eternal Life! When we look at the Kings, none of them lived more than 70 years - many were killed off quickly. Zimri after only 7 days! The priest, Jehoida lived to 130! (2 Chr.24). But God had a good reason for that - he was protecting and advising the good King, Joash. Similarly God has a very good reason that the patriachs lived to 175, 180, 147 years. God is NOT the God of Abbie (killed in a motor-cycle accident aged 45), The God of Issy (died of TB aged 39), the god of Jack (died fighting in the Somme). What sort of god would that be?? He is the God of the Living. Of course the patriachs lived very long. Note that Pharoah was amazed to hear that Jacob was 130, and Jacob told him that was nothing compared to his ancestors! This is a fact. It is not a fairy story. God is the God of the impossible.

Oops, got timed out by the computer, trying this again: In Genesis, the earliest patriarchs' individual lifespans are expressed the following way: "...the days of [name] were [number of] years, and he died..." The exception to this being Enoch, "...and he was not, for God took him." Similarly, Pharoah asks Jacob, "How many are the days of the years of your life?" (the difference there being he had not yet died). It's interesting that God uses the same idiom for "man"/humanity: "...yet his days shall be 120 years." Until God decided that, there had been no common maximum lifespan for humans, other than they seemed to die short of a thousand years, nor was any specific date given for when this descreased lifespan would start for humankind.

I read, of course, some years ago of scientists' discovery that the approximate, NATURALLY optimum lifespan for THE human body is 120 years: now God can alter this ordinance Himself for individuals for His own purpose, as He does for other ordinances (i.e., Enoch spared the common sentence of physical death for all humans), OR humans can medically alter it with ever-developing technology to rejuvenate human cells; nonetheless - but for godly or human intervention - 120 years is the natural optimum age the body is capable of on its own - barring poor diet, toxins that weaken our immune systems, disease, warfare, etc., that cause most of us to fall far short of that natural maximum age.

The most likely scenario: God said: “My Spirit will not contend with humans forever, for they are mortal; their days will be a hundred and twenty years.” About 20 years later God instructed Noah to build the ark. When Noah finished building the ark 100 years had passed, as it shows us in: Genesis 5:32: And Noah was five hundred years old: and Noah begat Shem, Ham, and Japheth. and: Genesis 7:6: And Noah was six hundred years old when the flood of waters was upon the earth.

But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
Genesis 2:17 (KJV)

A fixed human lifespan did not exist until Adam ate of the tree of the knowledge of Good and Evil. Likewise, a limit on this human lifespan did not exist until God proclaimed it. Finally,

And seeing a fig tree afar off having leaves, he came, if haply he might find any thing thereon: and when he came to it, he found nothing but leaves; for the time of figs was not yet . And Jesus answered and said unto it, No man eat fruit of thee hereafter for ever. And his disciples heard it.
[...]

And in the morning, as they passed by, they saw the fig tree dried up from the roots.
Mark 11:13-14 and 20 (KJV)

This is the same mechanism at work in the proclamation of the 120 year lifespan for man.

It could be that he was alive before the time was shortened, and as you can see if you read through the chronology, the shortening of the lifespan happened slowly, generation by generation. This is backed up by how it coincides with the flood, at which point the level of oxygen in the air depleted (perhaps to do with the increase in water for the flood, combining oxygen molecules with hydrogen).

120 may or may not be strict but a rough age, the same as an average lifespan of humans. I mean these days, who lives over 120? A very few who die very shortly after. Remember this account was written thousand of years ago, when we're supposedly living longer each generation.

On kind of a side note - Genesis 7:11 In the six hundredth year of Noah's life, in the second month, the seventeenth day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.

It is a fact that there are almost unlimited stores of hydrogen under the sea and deep in the earth's crust. Fountains if you like.

I believe it is important to note, when looking at the records of the generations of Shem (son of Noah) who was born before the mention of 120 years, (maximum human life span). Shem lived for 600 years. Thereafter, the lifespan of his descendants declined, throughout the generations. Maybe what God was saying was that, the lifespan of a human would gradually decline, until it reached 120 years.

I do not know where I read this idea - but it is not my own.

For some of God's decrees, there is a four-part implementation:

1. Decree given
2. Example made
3. Waiting period (for mercy)
4. Full implementation

The first example is the prohibition against eating from that tree in Eden.

Adam and Eve were told that "on the day you eat of it, you shall surely die". They did not die on that solar day - they died near the end of that prophetic thousand-year day:

A thousand years in your sight are like a day that has just gone by, or like a watch in the night. (Psalm 90:4)

So the decree was God giving the law against eating the fruit, the example was the death of Abel at the hand of his brother Cain, proving that death had entered the world, the waiting period for mercy was about 930 years, nearly a whole prophetic 1000-year day.

Now we turn to the days of Noah and God's decree about shortening life further.

The decree was given in Noah's day, the example was the flood, which came 120 years later, showing that God was not messing around. Then we enter the 1,000 year waiting period. In mercy, God permitted many righteous people (like Job, Abraham, and other patriarchs) to live more than 120 years, but the maximum life expectancy kept dropping, showing a phased implementation. Then comes the kicker: if you follow the chronologies, the 1,000 year period of grace ended about two decades before Moses died. Moses was full of vigor and in perfect health when he died:

7 Moses was a hundred and twenty years old when he died, yet his eyes were not weak nor his strength gone. (Deuteronomy 34:7)

Moses is the last person in the Bible to live to 120 years. No one subsequent exceeds his age. Claims in human history since then of people living longer cannot be substantiated. In recent times, proper documentation is required by the groups that track records (like the Guinness Book of World Records). Since that started, claims of people living longer have been debunked.

Thus Moses - who received the Law (like the 10 Commandments) from God, also received the law of human longevity in his own person, being shown as an example of God's law entering its period of universal effectiveness.

In entire bible, there are factors that changes the "default" man's lifespan:

Exodus 20:12 KJV
Honour thy father and thy mother: that thy days may be long upon the land which the LORD thy God giveth thee.

Deuteronomy 25:15 KJV But thou shalt have a perfect and just weight, a perfect and just measure shalt thou have: that thy days may be lengthened in the land which the LORD thy God giveth thee.

Proverbs 17:22 KJV
A merry heart doeth good like a medicine: but a broken spirit drieth the bones.

Isaiah 65:20 KJV
There shall be no more thence an infant of days, nor an old man that hath not filled his days: for the child shall die an hundred years old; but the sinner being an hundred years old shall be accursed.

Luke 12:19-20 KJV
And I will say to my soul, Soul, thou hast much goods laid up for many years; take thine ease, eat, drink, and be merry. But God said unto him, Thou fool, this night thy soul shall be required of thee: then whose shall those things be, which thou hast provided?

And you read in the patriarchs endings, each ends "full of years" and Jacob states that their years are "few and difficult". It makes me think about quality of years over quantity of days.