European cats aren't native to northern america, and as result, they're quite an invasive species with significant harm to the ecosystem. But that's not just limited to cats, that issue applies even to different species of lawn grass.

The other issue is destruction of ecosystem in the EU, where cats are native and primarily used as scapegoat.

Both of these need entirely different solutions, but "don't let cats outside" is very oversimplified and just serves to divide people.