The public opinion on feminism, much like the public opinion on religion, has been tarnished by extremists. Most Muslims don't agree with the Taliban. Most Christians are not as extreme in their views as the Westboro Baptist Church. Most feminists do not want women ruling the world, with men serving us. People are afraid to call themselves feminist, because they associate the word with "feminazis" who are actually mysandrists.
Misogyny and antiquated patriarchal views hurt men just as much as women. The goal of feminism is to eliminate these problems. For women to be paid as much as men. For the father to have equal custody consideration, instead of the default being the children going to their mother.
One very important aspect of the feminist movement is doing away with rape culture. Rape culture hurts all genders, at makes it very difficult for victims to come forward about their attacks. Women, because they will be told that they deserved it because of what they were wearing, how much they were drinking, or where they were. Men, because they will be told that it wasn't rape, because, being a man means that you always want sex. Trans people are especially hesitant because there is a terrible amount of transphobia in the justice system, and they will told that they're freaks, and that they deserved their attacks because of that. These reactions are terrible. Any person of any gender identity should be able to say to another, "I was raped," and receive a response of "I'm so sorry that happened to you. Do you want to go to the hospital? The cops? Here, have some tissues," instead of "You deserved it/you wanted it".