There's a lot of discussion now in the black and Jewish community about loving your natural hair even if it's not the "white" beauty standard. This may be a stretch, but if OP's girlfriend is of a minority ethnicity she might also be offended because he's implicitly saying "You are prettier when you don't look like your ethnicity."

Note that this wouldn't be a serious issue if he weren't so insistent. I'm Jewish and I wouldn't be offended if my fiance preferred my hair straight. But if he started pressuring me to straighten it for just sitting around the house, I might get uncomfortable in a way I can't fully explain.

I might be oversensitive because I was bullied for my hair and just recently learned to love it.