I have a feeling this is going to devolve into semantics pretty quickly. But I'll try. Let's start with Wikipedia. Opening statement:
Semantics have nothing to do with this. There are actual, concrete feminist positions than people disagree with or oppose.
Example: Feminists assert that domestic violence is a gendered phenomenon, with men as perpetrators and women as victims. And if women do commit domestic violence, it is not as bad as when men do. E.g. The Duluth Model:
www.theduluthmodel.org/about/faqs.htmlMany people disagree with this claim, since there are literally hundreds of studies that show that domestic violence is equally committed by men and women:
http://www.csulb.edu/~mfiebert/assault.htmFeminists assert that it is the responsibility of all men, whether they commit violence or not, to end domestic violence against women. E.g. White Ribbon:
http://www.whiteribbon.ca/Many people disagree with this claim, as non-violent men have no responsibility for the actions of other men. Just as law-abiding women have no responsibility for the actions of other women who commit false rape claims.
Example: Feminists assert that the fact that most politicians and CEOs in America are male, proves that men are privileged and women are oppressed.
Many people disagree with this claim, as the first fact does nothing to prove the second claim. Just as the fact that most prisoners, suicides, workplace deaths, and educational drop-outs are male does not prove that men are oppressed and women are privileged.
Example: Feminists at a university opposed the creation of a men's centre, despite the existence of a women's centre (common in most schools), with flimsy arguments:
http://www.macleans.ca/education/uniandcollege/long-live-the-mens-centre/Many people disagree with this opposition. There are plenty more examples where that came from, including feminist groups protesting talks about men's issues, via immoral actions such as physically blocking entrances to buildings, and illegally pulling fire alarms to shut down events (which was a crime in the city in question).
I could go on for a long time, but the bottom line is that there are many, many feminist positions and aspects of ideology that are unpopular - for good reason.
So it is incredibly dishonest to claim that "if a person believes men and women should be treated equally, then they are, or should be, a feminist."