Neither of you are wrong, but I feel like you're also both missing the point a little. Pride Month is one month out of the year, but in practice basically every other month in the year is straight pride month, and that's a super messed up disparity. So go ahead and be proud of being straight if you want, just be aware that there may not really be as much to be proud of. I'm not going to say there definitely isn't because I don't know your life, but there probably isn't. People don't have to come out to their parents as straight. People aren't regularly discriminated against for being straight. We live in a society where it's difficult to not be straight. And overcoming that, living as anything but a straight person in spite of a world which can make it difficult to do so, is something to be proud of.

I'm very confidently straight, and secure in my sexuality, and I'm a little bit proud of that. A girl I was dating at one point painted one of my toenails pink, and my dad saw it a few days later. I knew based on some other comments he'd made recently that he suspected I might be gay. I am not, but he seemed to think I might be and was trying to figure out if I was, which was mildly hilarious. He sighed heavily, but all he said was "... You must be very secure in your masculinity", and I kind of thought about it and told him "Well... Yeah, I guess I am." So I guess I'm a little bit proud of that. I know people who are so stuck in this traditional gender role world that they can't even hold a pink bag which is clearly a gift for someone else for a few seconds while someone else gets out of a car. That's just lunacy. What are you afraid of, that holding a pink object for a few seconds will turn you gay or something? So yeah, I'm somewhat proud that I'm straight and secure enough in my sexuality to step outside of traditional gender roles without feeling like my sexual identity is threatened. And if that sort of thing, or something like that, is all you're saying, then cool, be proud of that.

It's good to be confident about who you are, provided you aren't a terrible person, and it's ok to be proud of having attained that level of confidence. But I'm not going to pretend that there were any special barriers I had to overcome in order to live as a straight person in the first place.