Magical Artist Fantasy stuff that would never actually work.
I mean, you can choose your gender in the game, and Air Groove doesn't exactly change her attitude if you (her trainer) is male.
Then again she doesn't interact with any other male ever in the game (in her background story chapters she had a female trainer before quitting and then getting you as a trainer) so... that part of her background info is pretty much just fluff.
Though it is actually based on the IRL horse which did in fact have a problem with male trainers/handlers and preferred women. Plus, well, there was an incident when one of the male horses in a race she was in got really sexually excited because of her and freaked her out enough to lose the race...
Also, this comic here I believe is based on an actual event in Air Groove's game training story, where you do in fact meet her mother and talk about Air Groove for a while, embarassing her (though in more normal terms, no marriage talk). The comic is just explanding on that event.
Strange. Air Groove is stated to have "an uncompromising hatred to men". I wonder this trainer did to get her to warm up to him.
Her original JP profile initially mentions "she hates men because of a certain traumatic incident in a race" (レース中のとあるトラウマが原因で男嫌い). This line was subsequently removed.
Could be because of potential unfortunate implications and some logical inconsistencies considering all umamusume racers are female regardless of their real-life counterparts. But I'm not privy to Cygames' decisions, so this is just speculation.
The anime and game don't play up this character trait, so it's probably no longer there as a character trait (beyond the earlier planning stages when they drafted up her initial character bio).
Edit: There is another version of the profile with the line 「ちなみに潔癖症で大の男嫌い。かつて出走したレースで、何やらトラウマになった出来事があったらしい。」that seemed to have circulated around in 2018. This is much more strongly worded and is likely the origin of the "uncompromising hatred to men" line.
TL;DR: Air Groove was 'retconned' to no longer hate men. But EN fan wiki is not updated to reflect this.
Updated
Oh dear, Air Groove - do you hate Trainer-san? Hey, Trainer-san?Yeah, I got it.My darling Air Groove... wouldn't you like to have her as your wife?This girl, see, she's always talking about you on the phone, you know?Wha?She's sooo uptight that none of them stick around, see!Oh yes! She's never been good with men, you know? Never could get those bonds made!Haha, I get what you're talking about!Well... they're getting along fine, which is reassuring...My! Hearing you say that makes her dear mother feel so happy!I've gotten well used to this conversation from her...Though, speaking as the one that's in charge of her - that's just part of her charm!And in such glowing terms, too!I can quite confidently say that she's head over heels for you, you know?You're the first man that she's ever made a connection with, even!It's not like... that...Wait!That's not the issue here!I'll be waiting for the announcement from you two then, okay?You're not in the position to be thinking about those things yet, are you!Mothers are Strong...Air Groove as my wife, huh...?...a man can dream.What, are you just going to take her word on this!?MOTHER!!