You’re missing a little bit. You see, feminism is about equality across all genders – that is, it fights against the effect the patriarchy has on men.
For example:
– Due to the assumption that childcare is a woman-only concern, and nothing to do with the father, feminists frequently concern themselves with giving men longer paternity leave, not only so you can support your partner, but also so you have the time to fully commit to bonding with your new child and getting used to their continued presence in your life as well as your continued presence in theirs. Also for the same reason is changing the fact that baby-changing facilities can only be found in women’s public bathrooms (that is, if you’re able-bodied and don’t want to have to use the disabled facilities and inconvenience someone who actually needs them). For single fathers and fathers taking their children out without a female companion on hand, this can actually be a huge deal and lead to many a stressful situation, so the hope is to add baby-changing facilities to male bathrooms.
– Due to the stereotype that emotions are weak/female (these two qualities somehow interchangeable here, as per), millions of boys grow up believing that they can’t express themselves in an emotionally healthy way, and that they have to resort to violence to seem ‘tough’ and ‘suck it up’. Feminism wants to teach new ways to raise boys, to show them that everyone has emotions, that it’s fine to express them and they don’t make you weak, that it’s fine to cry. Not only could this lead to happier, more fulfilled men, but also to a lowering in violent crime, crimes of passion, less gang-related violence, and generally better anger management all around (sociological research shows that many men go into crime as ways to fulfil a social contract forced upon them to be as masculine as possible through economic and career-related success. If they cannot reach it through legal means due to various obstacles such as class and/or racial oppression, crime becomes a way to compensate (this is all theory, though)). By teaching better ways to ‘be a man’, we can make life happpier for everyone.
– Due to the degradation associated with anything remotely female-related, such as submission, being penetrated during sex (welcome to homophobia), and being a victim, male victims of rape are less likely to report their attack and seek justice. Why? Not only do they have to suffer such a harrowing, devastating violence on their person, they also have to suffer the shame of their attack being seen as a punchline, especially when their attacker is female (and not fight me on this – if someone forces you to have sex against your will, that’s rape, and regardless of the attacker’s gender or genitalia, they’re a rapist). Not ONLY that, but do you know what often happens when a woman starts a conversation about rape on the Internet? “Men get raped, too!!!” Male-victim rape only really gets brought up these days when it’s to refute a feminist trying to talk about female-victim rape as linked to female oppression, and do you know what that says when a person gives that refute? That they give less of a shit about male-victim rape than they do female-victim rape. Many male victims go unheeded, and that’s what feminism wants to change.

I know, I’m ranting. The deal is, I heard you say that you believe that Feminism, while great, doesn’t seem to you to be fighting in men’s corners, and you felt a bit like a gender-traitor for rooting for Feminism as a result. So, I gave you just a few examples of how Feminism is fighting for cis-gendered men. Yes, Feminism is quite happy to say how cis-gendered men have all this privilege, but what I want to underline is that we should all recognise that cis men have only been acting this way because the society cis men grow up in are teaching them ways to be male that destroy everyone INCLUDING themselves. I could go on all day about how it affects everyone else, but we need to highlight how it affects cis men, too. No, cis men aren’t oppressed, but they’re still suffering as a result to a degree that needs to change.

I just feel like they weren’t being wholly truthful with their stories.

What does this even mean? How do you “feel” someone isn’t being “wholly truthful”? Can you back up the “feel” with anything?