Well the other option is letting them starve to death, wander into streets and get hit by cars, or succumb to various diseases as a result of malnutrition. Like us, they don't know when to stop breeding. Naturally they are part of the food cycle for a lot of creatures that have died off. I don't see it as justification, I see it as 1) part of the natural cycle of this planet and 2) the humane option to letting them suffer.
If there were thousands of wildcats still roaming the forests in N. America then there would be far fewer deer for us to both cull and protect. Sadly those majestic creatures are almost completely gone and it is very illegal to kill them anywhere, yet they've got so little land to survive and thrive in they're just slowing dying and that is mostly our fault.
The gators down here in Florida are the same as deer, in fact way worse than deer. For years they were over hunted and almost extinct, as a result we protected them to the point that I have at least 4 in my yard a year. Reluctantly the legislature 'bent' to the scientists and opened up a bag limit of 1 per year with an extremely limited number of licenses available about 10 years ago. The gators are still breeding out of control and they have very little natural food down here anymore but they're doing better than they were while protected. They were eating pets frequently and also turning up dead from starvation, or swimming up on a shore they can't survive in, which they still do from time to time.
Oddly the deer here in Florida are almost extinct, yet the season is more open than Missouri's, which I strongly disagree with not just to protect them but because the gators need them for food and the deer would fare better being left alone to run from gators.
What blows my mind is how for some reason people think it's better to divorce ourselves from being a part of nature rather than to identify our role in it. Like it or not, skyscrapers are just as much a part of our natural evolution as ant hills are natural in the grass. They live and work in those tiny buildings made from the nature around them, just like we do.
I think we'd have a much better understand of our planet if we quit trying to shoulder the blame for all it's ills on ourselves as a means of protecting it, and instead opted understand our role and participate both giving and taking as needed for both us and nature. If we do so we will continue to be the apex predator on this planet for a lot longer than we're headed for now. We practice both over consumption and over protection. We only react to extremes instead of trying to reach a balance, which in the end is much healthier.
One day a volcano, comet, asteroid, sun spot, or something maybe even us; will eradicate a majority of everything on this planet likely including us. Over time it will rebuild a new species list vastly different from what we have now. We are the new Dinosaurs and in millions of years there will be some creature studying our bones and artifacts wondering how we survived so primitively with such small brains in comparison to theirs.
To hunt for food is "natural" in my opinion, if forced I would do so. For humanity to protect another species by carefully culling a small portion of it to prevent it's own eradication is far more compassionate than any other species on this planet. To hunt because you want a dust collector trophy on your wall, stupid and archaic thinking.