This, it's probably something like "Someone you like/love" instead of "Precious Family" since both can carry the same meaning but the specificity of "family" was the important part Tanuki wanted to convey (since Komaru has imposter syndrome regarding her place in her new family situation) so while he may still "love" her in a platonic (maybe more? Friend-kun seems to realize it goes beyond simple family affection) the implication of the slip is probably more along the lines of romantic love (Suki can be used for things you just enjoy/like but also used to convey romantic feelings).
He could still pick his sister but then he'd have to specify that it's a familial love which puts him and her in the spotlight with people making assumptions like they've already rampantly been doing. That said, I've been going to bat for Mochizuki for a while now and the author is not making it easy to defend her when she's consistently written more and more deviously. Either have her go full villain or stop teasing the readers.
I've been enjoying them for the most part but this one is a bit too sanctimonious to the point that it misses its own point. Promiscuity in and of itself isn't really a "negative" qualifier, it just means a person enjoys sex usually with multiple partners. It's a real term and using it doesn't imply a person is demeaning the person they are calling promiscuous, it's just a statement of fact. A better term would be "Slut" or calling someone "easy" which has the negative implication you're implying here.