Feminism is about people being treated the same way regardless of their gender. Women historically and currently face more obstacles than men so by sheer coincidence feminism does focus on womens issues a lot more, and that should be the case because of they're the more subjugated gender.
Egalitarianism is about people being treated the same way regardless of any particular. Feminism is about both men and women having equal rights, but it's a movement based around gender and as such it is different to egalitarianism which focuses on more than gender. Saying you're an egalitarian but not a feminist is like saying "well, I don't really care for those anti racism campaign, see, I'm an egalitarian so I do things better", it's not only ridiculous but it completely undermines the position you're taking.
Oh my god, you live with a feminist. You definitely know everything about feminism now. Anyone who says "I don't need to read anything else" definitely needs to read more.
Women's problems are definitely bigger. Women not getting equal education and opportunities is the single biggest factor leading to poverty. How is that not a bigger problem than what men face? There are few countries in the world where women aren't treated as the inferior sex.
Most men are sexist though. Most women too, coincidentally, but men more so. It's a pretty big world and we're not all Swedish.
The majority of men in 2014 are still pigs. There is a lot of need to raise awareness for women's equality as women not getting equal opportunities is one of the main reasons there is poverty in much of the world. The pay gap still exists in developed countries. Rape culture is a thing. Women aren't particularly well represented in the arts. And society as a whole still treats them like second rate citizens.