People don't disagree with equality (of opportunity), but with feminism actually being for equality instead of privilege. Basically what they see is feminists who preach equality but their actual actions paint a very different picture.
Take a look at the Duluth model, based on feminist doctrine. which severely discriminates against men who are victims of domestic violence (women are just as violent as men, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1854883/) by assuming that men by default are the aggressors and having the man who called the police for help arrested even though he is the wounded one.
Take a look at how there still is affirmative action for women in colleges even though women nowadays earn 58% of college degrees.
http://www.statista.com/statistics/185157/number-of-bachelor-degrees-by-gender-since-1950/
Take a look at reproductive rights - feminists ask for more of these for women, yet men have NONE. Women can legally surrender parenthood without the father's consent even after birth, while men cannot ever do this - not even if the child was conceived by an illegal act of the mother, such as statutorily raping a boy. Here is an example of a boy who was statutorily raped being sentenced to pay child support: https://en.wikipedia.org/wiki/Hermesmann_v._Seyer
How is fighting for even more reproductive rights of women and ignoring those of men equality and not privilege?
Take a look at calls for gender quotas in the workplace - pretty much always for nice white collar jobs. Why not call for quotas in ALL jobs? That of course may then also include the nasty ones, such as sewer maintenance. But doesn't getting an equal share of the nice jobs also mean that one must do an equal share of the dirty work?
Asking for quotas only in the nice jobs is asking not for equality but for privilege.
Take a look at how sexual abuse of men in general is treated. It's ignored and victims of it are ridiculed. Men generally don't have access to the DV shelter structures despite of paying their share in the funding thereof.
Take a look at the sentencing bias between men and women for the exact same crimes and criminal history, which is greater than that between blacks and whites:
http://people.terry.uga.edu/mustard/sentencing.pdf
Yet feminists have the audacity to ask to have women sentenced to even less prison time than they already are, even suggesting to abolish women's prisons completely.
http://www.telegraph.co.uk/women/womens-politics/10015766/Isnt-it-time-to-abolish-most-womens-prisons.html
If that's not demanding privilege, then what is?
I could list some more issues, but i don't want to do a Gish Gallop on you. Please take your time to read up on these issues - preferably not only from feminist sources, but from the other side as well.