Domestic cats' population is orders of magnitude larger than the native cats population was or is.
While you're correct that humans are also devastating the habitats of native birds, and that that is likely a (much?) larger effect, the invasive species that is the domestic housecat is also talking a toll of a couple billion birds per year.
There are multiple well-regarded studies providing those numbers. You choosing to disbelieve them is about as valid as believing vaccinations are more harmful than diseases, that climate change is a hoax, or that illegal immigrants are responsible for the housing shortage.