You can get traps that don't kill mice and you just drop them outside and you both get to continue with your life.
Mice don't understand the difference between a house and any other shelter, you couldn't invite them into your house if you wanted to because they don't understand your language.
Humans can deliberate between life and death, that's the difference.
When it gets to infestation levels a humane resolution regrettably has to be sort.
Living near a river and surrounded by the countryside we get a lot of wildlife entering our house, some of them (spiders, moths etc) stay until their lives are at risk (at which point I put them outside if I can) others like mice, rats, lizards, frogs etc are taken outside where they hopefully find a better home.
The starlings we couldn't move even if we wanted to because nesting birds are protected by law.
Once they moved out we repaired the damage and tried to secure the vents better but we couldn't touch them while they were there and wouldn't want to anyway.
Millions of spider babies chewing through the ceiling was a sadly a job for the professionals.