It is not humane treatment of animals to place a killing machine in their midst. Nor is it humane treatment of animals to allow one to live, with the knowledge that others will die painful deaths because of that act.
The damage that outdoor cats do to populations of birds and other wildlife has been documented and fretted over for a long time, and it's always made me worry that the trap-neuter-release programs for feral cats -- cats that are genetically domesticated but that have essentially returned to being wild animals -- are inadequate. The released cat might be unable to reproduce, but it has many years ahead of it to kill birds, voles, lizards and other animals.
Now, the most comprehensive study on this subject -- large-scale, peer-reviewed, commissioned by the U.S. Fish and Wildlife Service -- finds that things are even worse than we'd feared. Here's the money quote: "We estimate that free-ranging domestic cats kill 1.4–3.7 billion birds and 6.9–20.7 billion mammals annually."
Some of those are family pets allowed to wander, but the majority are, so to speak, homeless cats. The findings suggest that people's willingness to let cats roam free is the single biggest source of human-caused wildlife death.