FWIW, I abhor any mistreatment of animals, but the deer population needs to be dealt with.
As 'humanely' as possible, but dealt with.

To answer your question, nearly all of deers' natural predators have been eliminated by human activity. This has thrown off the natural balance of course, and the result is that deer populations have exploded.

Because of this overpopulation, many starve off-season and there's nothing 'humane' about that either.
Can we lace deer food with contraceptives?!