If that were all there was to feminism, there would be no controversy. There is a lot of controversy.
P -> Q
This response was apparently not welcomed because the skeptic was then compared to a misogynist trying to put women back in the kitchen.
The problem is, the skeptic was right. If feminism simply meant someone who supports gender equality there would be very little controversy except for a few very backwards people. There is, however, much controversy, and that supplies evidence that there is much more to feminism than simply seeking equality. This is the reason there are people who say "because I support equality, I am not a feminist."
The problem is that feminism, and feminists in general, refuse to own the radicals in their own movement.
Take the case of Westboro Baptist Church, famous for picketing funerals with anti-gay propaganda. Many Christians are quick to say that the members of that church aren’t "true Christians," a response that has caused Antony Flew to describe the "No True Scotsman" fallacy. A fallacy or not, it does show that the speaker believes that the members of the Westboro Baptist Church are not demonstrating the way a Christian should behave.
With feminism, there is a different response, and it is not even up to the level of a No True Scotsman fallacy. This response is so common it has even been given an acronym – NAFALT. When confronted with something radical said in the name of feminism, apologists will say "Not All Feminists Are Like That."
Take the case of Youtube Vlogger Femitheist, who made a video that appears to advocate androcide, reducing the male population to 10% of its current numbers. Rather than say "yes, that is a position taken by feminists" or "no, that is not a position taken by feminists" the speaker seeks to simultaneously embrace and reject the radical position.
It is this refusal to own the issue, by either acceptance or rejection, that confounds those who would wish to be allies if feminism was what advocates claimed it to be, because the positions taken by the radicals are clearly not positions that advocate equality. If the "mainstream feminists" were to take a position, for or against, the radical positions then those who do not consider themselves to be feminists and consider themselves to be supporters of equality can finally come down one way or the other with regards to feminism.