Would you yourself consider lifetime seclusion? Why, you cause harm to billions of living creatures every time you venture outside. (Although sitting in solitary jail cell only reduces that by a negligible factor). And that's only taking into account direct harm, third or fourth-order consequences of being out there are impossible to even start comprehending.
If not, why you think it's okay to condemn another living creature to such a life sentence? After all, its well-being is just as important as yours, is it not so?
It's pretty clear its well-being is not just as important as ours — as a society we have decided this; we don't give cats open-heart surgery, it's not illegal to kill a cat, and cats also have no rights.
Cats seem pretty alright with "lifetime seclusion", anyways. As with other domesticated pets, the only reason they exist is because they are, on the whole, happy being domesticated; if they all hated their lives (in a way that we were aware of), we wouldn't breed them to begin with.
