> instead of just not breeding more

As one might guess, the "just" there is doing a lot of work.

Common pets reproduce just fine without our intervention - in practice it requires costly maintenance programs just to keep their population under control (not to mention the massive and ongoing eugenics program required to produce only the desirable breeds/attributes).

If your neighbourhood isn't overrun with stray cats and dogs, that's because someone is funding a spay/neuter program, and someone is funding animal control to round up (and ultimately euthanise) the rest.

All animal husbandry systems have to be maintained via regular culling, and "eliminating" pets would require orders of magnitude more killing

I always assumed the "enslaved animal-free" future would be something that came on gradually, likely motivated by economics (i.e. lab-grown meat becoming cheaper and higher quality than farmed, robotic pets being cheaper and more "trouble-free", etc).

I never felt like anybody seriously thought we'd release domestic animals into the wild to fend for themselves-- that's ludicrous.

yup!