First, a definition,
the advocacy of women's rights on the grounds of political, social, and economic equality to men."
-The Oxford Dictionary, 2nd Ed.
What is so controversial about that?
Feminism has brought us birth control, women's work protections against harassment, and progress towards equality with men in general. What's so horrible about these things?
Certainly, there are some "feminists" who tend to exaggerate problems with men and be hostile towards them, but they go beyond the standard definition of feminist; most feminists criticize patriarchy and how it favors men over women which fits the definition.
So, what's the problem with feminism?