This is a simple question with a complicated answer, because there are varying degrees of, and reasons for, animosity between any two religious groups. The battle between Catholics and Protestants is rooted in history. Degrees of reaction have ranged from friendly disagreement (as reflected in the numerous ecumenical dialogues produced between the two groups), to outright persecution and murder of Protestants at the hands of Rome. Reformation teachings that identify the Pope as the Beast of Revelation and / or Roman Catholicism as Mystery Babylon are still common among Protestants, anyone with this view is not going to “warm up” to Rome any time soon.
For the most part, today at least, the animosity comes from basic human nature when dealing with fundamental disagreement over eternal truths. Passions are sure to ignite in the more weighty matters of life, and one's faith is (or at least should be) at the top of the heap. Many Protestants think Roman Catholics teach a works-gospel that cannot save, while Roman Catholics think Protestants teach easy-believism that requires nothing more than an emotional outburst brought on by manipulative preaching. Protestants accuse Catholics of worshipping Mary, and Catholics think Protestants are apparently too dull to understand the distinctions Rome has made in this regard. These caricatures are often difficult to overcome.
Behind the particular disagreements over the role of faith and works, the sacraments, the canon of Scripture, the role of the priesthood, prayers to saints, and all the issues surrounding Mary and the Pope, etc., lies the biggest rift between Roman Catholicism and Protestantism: the issue of authority. How one answers the authority question will generally inform all the other issues. When it comes down to deciding a theological issue about defined Catholic dogma, there isn’t really much to discuss on the Catholic's side because once Rome speaks, it is settled. This is a problem when trying to debate a Roman Catholic – reason and Scripture are not the Catholic’s final authority; they can always retreat into the “safe zone” of Roman Catholic authority.
Many of the arguments between a Protestant and a Catholic will revolve around one's “private interpretation” of Scripture as against the "official teachings of the Roman Catholic Church." Catholics claim to successfully avoid the legitimate problems of private interpretation by their reliance on their tradition. But this merely pushes the question back a step. The truth is that both Roman Catholics and Protestants must, in the end, rely upon their reasoning abilities (to choose their authority) and their interpretive skills (to understand what that authority teaches) in order to determine what they will believe. Protestants are simply more willing to admit that this is the case.
Both sides can also be fiercely loyal to their family's faith or the church they grew up in without much thought to doctrinal arguments. Obviously, there are a lot of possible reasons for the division between Catholicism and Protestantism, and while we should not divide over secondary issues, both sides agree that we must divide when it comes to primary issues. When it comes to Roman Catholicism and Protestantism, the differences are just too great to ignore. However, that does not give license for caricatures or ignorant judgments – both sides need to be honest in their assessments and try not to go beyond what God has revealed.