I'll take the RSPB's advice in the UK (there is little/no evidence cats are having a harmful effects on bird populations in the UK, tall buildings may have more effect, pollution definitely does, other forms of habitat destruction even moreso, etc.), though my current boss is happily an indoor cat.

In places where cats are essentially an invasive species, not native at all, this is different of course.

Feral cats outnumber domestic ones 2:1. Do humans affect that? Feral cat populations grow to fill their niche, with or without humans. I don't see how domestic cats account for more than a small fraction of the issue.

And again, when bird populations reach equilibrium the cats can't find more. That's independent of cat populations.

Feral cats are domesticated cats that have escaped and are no longer considered domesticated. The point is that if it weren't for humans we wouldn't have so many feral cats.

Also, feral cats tend to congregate close to human populations.

I'm not sure what your point is about equilibriums. Of course equilibria are reached naturally, but with the human factor these equilibria have been distorted beyond any natural capacity. In short, any human-impacted equilibria tends toward the rapid decrease in species populations, often to the point of species extinction.

Not at all sure that's sound reasoning. What have humans to do with feral cat populations? Sure a few domesticated cats escape every year, but that just temporarily perturbs the feral population which is self-adjusting.

Definition of feral (from google): (especially of an animal) in a wild state, especially after escape from captivity or domestication.

There may have been inter-breeding involved with wild populations, but most, if not all, feral cats have their origins in domesticated, or captive (by humans), cat populations.

Also, have you ever noticed that feral cats tend to congregate near humans? That's because they find it easier to find food from dumpsters, handouts, garbage, etc. This is very similar to other species that rely on humans for their success (rats, corn, cockroaches, crows). This artificially increases their numbers. I say "artificially" because their food source comes indirectly or directly from humans.

So simply from the definition of the word "feral", and not even including the inter-species dynamics between humans and feral cats, humans have everything to do with feral cat populations.

Probably refering to available resources for feral cats, it decreases with more domesticated cats out hunting.