from what we see across all of Trek, pet ownership, in general, simply doesn’t seem as popular as it is today. perhaps it went out of fashion and is an eccentricity practiced by the few. perhaps it’s simply a biased reflection we experience due to the fact that we mostly only see space-born folx and toting around another living thing with you while trekking across the stars is a terrible inconvenience best avoided. that might explain why the only time we see people with pets, they’re almost always a senior staff member/officer with a long-term posting. or some civilian living in a house on a planet.

remember, Riker was first tasked with watching Spot for Data, and he couldn’t handle it at all- and he was 100% human who grew up on Earth. Geordi flat-out refused to even try looking after Spot.