I never got why yukkuri owners killed their yukkuri for refreshing without permission. I would personally put them up for adoption. The fact that their children would live but never know their birth parents would be more enjoyable to me and more cruel to them, in my opinion. Which is not to say we know for sure if that's what happened here, of course. Just a general observation and commentary.
Because in general it's believed, for good reasons, that when a yukkuri doesn't respect the "no refresh rule" that means it will start disrespecting other rules, or that the yukkuri you got wasn't good quality, plus, the scenario of "punishing the refresh with death" is usually about pet + stray pairing, since those usually corrupt the pet.
Pets refreshing is a bit more complex, while there is the whole "they didn't respect the rule", a pet may not necessarily turn worse for disrespecting the rule and the negative influence of the stray yukkuri.
Chen and Shou parents refresh against them mister's rules, so they run away since they know they would bring extra problems to the mister.
In their life as strays, they may had got abused by either fellow yukkuris, or abusive anons, only for the owner, to somehow find the chen again with the babies and proceed to save the babies.
Somehow he may had recognized the mother and now compares the kids with his late pets.
Red_Ruin said: Did the owner kill the parents? The impression I got was that the anon found mother Chen's corpse after she had been abused by someone else.
Kinda left unexplained at this point. He could have, he could not have. I just thought I'd start an interesting discussion while I was at it (as it came to mind) while noting he may well have not killed them himself.