@Epsilon04, if not asexual, not with any kind of trauma, and hopefully with a good experience of sex (read as: they are respected by their partner during the act) people don't usually find sexual skinship as gross. but that's not even the point tbh. it often happens that, when in desperate need of affection, the person will accept basically everything from their partner, even if not really wanting it, and will see whatever action as an expression of love. many toxic relationships are born right because the person sells their freedom and self esteem for something they want to see as comfort.
maybe the girl in the manga just wanted a big hug and someone who'd tell her she's worth. sadly, often sex is seen as the most straightforward and simple way to determine one's worth. the idea is that if someone doesn't find you gross and is fine with touching you to the point of having sex, then you probably aren't as bad as you feel. it gives you that "i got chosen too", "i'm needed", "i'm able to give satisfaction (even if maybe i myself don't really enjoy it)" vibe.
this is obviously a very difficult topic and there's a wide variety of relationships, reasons and outcomes, so i wouldn't want to generalize. what i said mostly comes from personal experience and i thankfully had it super light. but yea that's usually how it goes, especially when the person didn't get a chance to mature and is really young.