The main reason for that, is because I think that feminists aren't actually fighting for equality. Otherwise, they would address issues that make them more priviliged than men, so that they would become truly equal to men. For example, men are more likely to be incarcerated for longer periods of time then women, even when they committed the exact same crime. I could give you another example about domestic violence in the UK. There, 40% of domestic violence victims are men, but at the same time, the spots available for men in domestic abuse shelters is barely 2%: 80 spots for men, 4000 for women. In short, as long as both female and male privilege exist, true equality will not be attainable.
Yes! Yes there are issues! And yes they're addressed by feminism! Patriarchy affects men just as much as women. Why do you think there's always the image of men being strong, emotionless, quick to violence? Because that's what our society has deemed 'masculine', a trait assigned to them just like 'feminine' traits are assigned to women. The courts give kids to women? Because women are supposed to be the caretakers in our society's eyes. Domestic case? Well it has to be men, because our society's perception is men are strong, women are weak. If you look up any feminist rhetoric, these are issues frequently addressed and brought up. These things are important, but the people who spout 'feminists don't care about equality' have never investigated feminism, they only know what they've been told about feminism from people who hate it.
I completely agree with your first paragraph. However, it seems that the most vocal, and also negative feminists (perhaps a minority), attract more attention than the ones who address the issues you mentioned above. At the same time, you can find plenty of stories online about men who think that women shouldn't be allowed to vote or that they belong in the kitchen. We can only progress by making both of these groups aware that their hate-mongering is only pitting different groups of people against each other and is not leading us anywhere.
All I get from this is that both men and women have problems. And I certainly agree with that. And I can also agree that the issues men have should be solved, too. But I don't think being okay with feminism and solving those problems for men are mutually exclusive.