The term “feminism” is controversial for at least two reasons.
First, there is controversy as to what the term should mean. That is, different women define feminism in different ways. There are conservatives who see themselves as pro-woman, but who do not think that feminism should ideally refer to the liberal ideas of most feminists. This aspect of the debate is likely to surface in the discussion over the recent change that would allow women in combat in the US military. There are feminists who have different theories about what constitutes women’s empowerment. This debate is particularly prevalent with regard to issues of sexuality. Different women disagree was to what feminism should mean when it comes to things like how women should dress and how they should portray themselves in sexual terms.
Second, there is controversy simply because the term “feminism” has been used by conservatives in a strongly pejorative way. Conservatives often portray feminism as an ideology that is anti-male. Liberals would argue that conservatives have created a false image of what feminism really is and that conservatives use that image to demonize women who want more in the way of rights.
Feminism, then, is controversial for these two main reasons.