Women in the infantry

I (27F) got into a fight with my husband (23M) last night after he told me that women don’t belong in the infantry (army).

He’s in the infantry, I am not (just finished my graduate degree). In response to me pressing him about why he doesn’t think women belong in the infantry the only cogent rationale he came up with was that in a battle scenario a woman couldn’t carry him or other large men. (Though I don’t think this is true across the board as there are plenty of scrawny men and plenty of large and strong women)

His other, in my opinion incredibly sexist and illogical, arguments included that a woman could be on her period, that women are more mentally fragile, and that women can’t physically carry a ruck and a machine gun as he saw many women drop out of basic because their hips were breaking under that stress.

He tried to soften the argument by saying that he can’t do what I do and I can’t do what he does. To which I pointed out a crucial distinction is that we both agree he can’t do what I do because I went to school for 8 years to be qualified, but he’s trying to argue I can’t do what he does solely because I’m a woman.

The argument finished with me saying that someday he’s going to have to tell our daughter that he doesn’t think she can do certain things solely because she’s female and I hope he understands by then that that is messed up.

I’m just looking for some other people’s opinions - was I being overly sensitive? How should I try to explain this to him without him just seeing red and getting angry?

Edit: thank you to everyone who responded! I have an update after he and I revisited the conversation post cooling off- he apologized for being defensive and stubbornly trying to come up with an argument and acknowledged he was being sexist. When I pushed him on why what he said was sexist he responded that any woman that can meet the standards and wants to be in the infantry should be able to. The rest of his comments were coming from a patriarchal viewpoint that the army is a toxic place in general in some respects but that it is uniquely dangerous place for young women and that he doesn’t see it changing for a slew of reasons.