I have killed at least a dozen deer with a .22-250. It can be done.
That said, I prefer more power, so I use a .30-06. I've had a few long tracking jobs with the .22-250. Tracking a deer is great fun, but it probably isn't the most humane way to do things, so now I use a bigger stick.
For those who are patient, careful about shot angle, don't overdo it on range, and don't shoot at running deer, a .22-250 is perfectly fine for deer.
I prefer larger caliber because I don't want to worry about shot angle, sometimes hunt at long range, and sometimes shoot at running deer.
I don't understand why some people think that because they do things a certain way, everyone else should too.