Is this weird or am I just overthinking

So my bf (24) and I (23) are expecting our first baby (a boy) together. So when my bf was 16 his then gf got pregnant and had a baby girl. He helped raise her for the first year until she told him she cheated on him and the baby wasn't his. He then said she left and wouldn't let him see the baby or anything and it broke him. (I did look at her FB to see and she says she has a DNA test for the baby girl (whose now turning 8) and knows who the father is (a different guy then my bf) and he wants nothing to do with the baby girl and she posted pics of the two side by side saying they're twins.)

Well my issue is that my bf still claims her as his daughter. Like when talking to a guy on xbox tonight he said "my girlfriend is pregnant with my son. It's my second but her first". Anytime anyone asks if it's our first baby he always says he has a daughter and this is his second and this baby is my first. It makes me uncomfortable. Like I would get it if he was still in the little girls life and was raising her (even if not biological) but he hasn't seen her in like 7 years. And there's no proof she's biologically his (even she was his by blood id consider him her sperm donor not dad because he's not and hasn't been active in her life in so long). I don't understand why he does this. I've tried talking to him he says he can tell she's his but hasn't fought to see her nor get any DNA test or reach out to the mom to see if she actually got a positive DNA test with the other dude. It just really really bugs me. Idk am I overthinking or is it weird?

Edit: I have encouraged him for years before we got together (we've been together almost 3 years) to try to fight for her, to try to get custody, a DNA test or even message the mom asking if the DNA test she got on the little girl is real. But he hasn't made any effort. I would even consider her his daughter if he was just active in her life and not biologically his. Idk if he just wants to be her dad that bad but is scared to see she's not his or what. Maybe because it's the first baby he's helped raise (even if for only a year). Idk I just find it weird.