Overpopulation in wild animals leads to the spread of disease to each other and also to people (75% of re-emergent human viruses over the last century have come from wild animal populations).
An overpopulation of predators also wipes out prey species and eventually causes a mass die-off of the predators themselves through starvation and competition.
Lastly, humans have wiped out most of the species that keep wild populations in check, like wolves. We created this issue, and sometimes we have to take on icky but necessary responsibilities for our actions as a species.
There is much more to this than what you can apparently see.