Why are the Immaculate Conception and the Assumption of Mary such a big deal that all Catholics must believe in them?

It is important for a believer to have a proper understanding of Mary in order to have a proper understanding of Christ. What do I mean by that?

Protestants always (I wanted to type "often") look on Mary with the idea that her role in the salvation of man is inconsequential or minimal. When doing this, they use the same scripture Catholics use to highlight her importance to actually diminish it. I can think of four scriptures that Protestants love to twist around and use as examples as Mary's insignificance to Christ: Luke 1:38, Luke 11:27, John 2:1-12, and Matt 12.

In Luke 1:38, Mary gives her permission, hearing the word of God, and obeying.

It is here that I think most Christians understand (or at least can't object to) the fact that the Mother of our Lord believed God and obeyed his will. So often in the commentary by anti-Catholics, her role is diminished here and her fiat was unimportant, suggesting that if it was not her, it could have been any other virgin - any incubator for the son of God would do. The Catholic version speaks differently; it speaks of Mary hearing the word of God and keeping it. Not only that, having understood the difficult and precarious position that the Lord would be putting her in, through her trust and belief in God, she chose by her free will to "let it be done to me, according to your will". The Protestant conundrum here is that everything is not God - it is not Jesus alone - but Mary who willingly united herself to the will of God. This relationship - the relationship required of all believers - threatens the doctrine of Faith Alone. It threatens the Church's position opposing double predestination and election. These doctrines are a perversion of the actual Gospel and the Truth of our roles as believers to not only be like Christ, but to be like Mary: to hear the word of God and obey, not because we are puppets on a string, but because of our own free decision.

Luke 11:27:

As he said this, a woman in the crowd raised her voice and said to him, Blessed is the womb that bore you, and the breasts that you sucked!

Again, we have a distortion that is perpetuated by the necessity of Protestant doctrine to diminish the role of Mary in the proclamation of Christ in answer to this statement whereas the truth is, in fact, in opposition to it.

Blessed rather are those who hear the word of God and keep it.

Anti-Catholic preachers so often use this verse to lessen the importance of the mother of God when Christ's purpose was not to lessen the importance of Mary but to address the real reason for Mary's blessedness. Any woman could bear a child and feed it; this is done by any woman who has children. This statement made from a shout in the crowd is the incubator argument made by anti-Catholic preachers. Christ clears this up for us; in no way is Christ lessening his mother's role, but clarifying it. Referring back to Luke's account of her fiat, Mary, not thinking of her own desires of the flesh, is blessed not because of her capacity to give birth and feed Christ, but because she heard the word of God and Kept it.

John 2:1-12:

Oh woman, what have you to do with me?

I often hear Protestants using this verse especially to demean the role of Mary, to suggest the Christ is putting Mary in her place. Biblically they will say, suggesting the Christ rebuked her in some way. I actually heard one separated pastor suggest that calling her "woman" was Christ insulting his mother. (Can you imagine?) From a Catholic perspective, Christ calling Mary "Woman" is how she is identified as the woman whose seed will crush the serpent's head. Genesis 3:15. "What have you to do with me?" The Protestants' answer to this is: nothing. The Catholics answer to this is: everything. Mary by her fiat, spoken of above, made possible by her freewill acceptance made possible the incarnation of the Lord Jesus Christ, and here at the wedding of Cana, as she did at the Annunciation, The Mother of God so sets Christ on his earthly ministry.

Matthew 12:46-50

here are my mother and my brethren

Again, the anti-Catholic, in desperation to reduce the importance of Mary that is proclaimed here in Scripture in order to establish the insignificant role of Mary and how she is actually rejected as unimportant to Christ ministry compared to the disciples, is ignoring the true message that Christ was bringing to the people.

It is commonly known among the Jews that the descendants of Sarah, wife of Abraham, whose children were of Isaac and inheritors of God's promise to him, were the mother's sons and the brethren of Jacob. (See Genesis 27.)

who is my mother, and who are my brethren

Stretching out his hand toward the disciples (followers of Christ) "Here are my mother and my brethren" indicating that the new mother was indeed Mary and her son and his brothers. The descendants of Mary, through faith in her Son not through biological motherhood but through discipleship in Christ, were his followers. The new Israel of God. As Sarah was the representative mother of the people of God in the Old Testament, so now, Mary represents the Church from whom Christ body came.

Conclusion: So why the ex-Cathedra pronouncements?

As with all dogmas of the Catholic Church, the dogmas of Mary were established in response to the heretical teachings and distortions of others at the time. In this case, the anti-Catholic, anti-Gospel teaching of the Protestants concerning the role of Mary and the Church made not only the Marian Dogmas necessary, but before that, the dogma of the infallibility of Pope. Prior to the falling away of so many Catholics, these dogmas were not necessary. The Dogmas state unambiguously the importance of Mary's role in salvation and her submission to God's will, which is an example to all of us. Mary, the first Christian, the first human to have Christ in her by Faith and obedience to God, is essential to understanding the Truth of the Gospel. The distortion of these truths had necessitated dogmatic pronouncements of the Immaculate Conception and the Assumption of Mary. These things have always been known, but the need to establish them as proclaimed dogma them had yet to develop. These pronouncements are not, as you imply somewhat dismissively, "such a big deal to Catholics". They are a big deal to all who follow Christ and who want to understand True Christianity. It is a Big Deal because the true message of Mary's obedience and the true message of Christ's love for her (and her love for Christ) had been (and continues to be) distorted especially by those opposed to the Catholic Church who will work very hard to convince people to separate from the Mother Church.

Revelation 12:1:

Then the Dragon was angry with the Woman and went off to make war on the rest of her offspring, on those who keep the commandments of God and bear testimony to Jesus.

Those who keep the commandments of God and bear testimony to Jesus are the Catholic Church.

Catholics believe that Mary was chosen, not so that she could be the Mother of God, but so that she could choose whether or not to be the Mother of God—and that in order to make this choice in complete and perfect freedom, she was redeemed from original sin from the moment of her conception:

In order for Mary to be able to give the free assent of her faith to the announcement of her vocation, it was necessary that she be wholly borne by God's grace.

Through the centuries the Church has become ever more aware that Mary, "full of grace" through God, was redeemed from the moment of her conception. That is what the doctrine of the Immaculate Conception confesses ...

At the announcement that she would give birth to "the Son of the Most High" without knowing man, by the power of the Holy Spirit, Mary responded with the obedience of faith ..., Thus, giving her consent to God's word, Mary becomes the mother of Jesus.

Catechism of the Catholic Church, paragraphs 490–491, 494; emphases added

The Church teaches that this belief, though not always formally articulated, dates back to the beginning of the Church. As the Word of God, it has come down to us in Sacred Tradition. To deny it would be to deny that Sacred Tradition is the Word of God, or even to deny that the Word of God is Truth.

To be clear, this was part of the depositum fidei, the treasury of the faith, even before it was labeled an ex cathedra truth. But it was something that was simply assumed to be obviously true: of course Catholics would, and would have to, believe it. Pope Pius IX declared it as dogma in 1854 in the bull Ineffabilis Deus (which, mysteriously, seems to be missing from the Vatican website).

In the bull, Pope Pius stated that among his reasons for declaring this belief as dogma were to show that the Catholic Church was the one true Church, regardless of the beliefs of other churches; and to put into a formal statement something which had been believed and declared by the Church since ancient times. He asked for comment from the bishops about whether he should make such a statement of dogma, and they concurred. Therefore Pope Pius wrote:

We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful.

Hence, if anyone shall dare—which God forbid—to think otherwise ... let him know and understand that he is condemned by his own judgment ...

In other words, the pope simply said that because of the antiquity and universality of the belief, it was a matter of Sacred Tradition, revealed by God. Such a belief cannot be denied without denying that God's revealed Word is Truth.

Something similar happened with the declaration of the Assumption of Mary, proclaimed nearly a century later. Again the pope (Pius XII, in his apostolic constitution Munificentissimus Deus reviewed a long history of belief that Mary was assumed into heaven, and interpretations of Scripture supporting the fact. He revealed that, just as his predecessor, he had asked the bishops of the world whether he should declare this belief a dogma, and they had responded overwhelmingly "yes". He therefore stated:

We pronounce, declare, and define it to be a divinely revealed dogma: that the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory.

Hence if anyone, which God forbid, should dare willfully to deny or call into doubt that which we have defined, let him know that he has fallen away completely from the divine and Catholic faith.

All this is perhaps just a long way of saying the following:

Why are the Immaculate Conception and the Assumption of Mary such a big deal that the popes, by speaking ex cathedra, require all Catholics to believe in them? Because the Church believes, and has believed from as far back as we can find, that these things have been revealed to us by the Word of God; and we cannot deny the Word without falling away from God.

Addendum: Based on a comment, it appears that the question is attempting to understand why Mary's assumption, as opposed to (for example) Elijah's¹, is picked out as being so important for the Church to emphasize. The reason is simply that Mary is so much more important to the Church than Elijah is. Elijah was, certainly, a holy man, among the closest to God of all major characters in the Old Testament. But he was not so pure and holy as Mary was. There was no particular reason for him to need to be sinless; there's not the compelling "appropriateness" for sinlessness that there is with Mary. Similarly, though he was also "caught up to heaven", it's not for the extreme intimacy of his relationship with God—a relationship that couldn't get much more intimate than that of Mother with Son. So it's much more important for the Church to emphasize the holiness of Mary than that of Elijah.

¹The original poster chose Moses as an illustration; but Moses died and was buried, whereas Elijah was taken up to heaven.