They rub their antlers on tree trunks in the fall because they are itchy. Over the summer they grow new antlers each year. The antlers are initially covered in fuzz. In the fall this fuzz becomes itchy on their antlers. Consequently, they rub their antlers on trees to remove the fuzz and make their antlers sharp.
Deer are vegetarians.
They do not eat other animals. This doesn't mean they are never violent. In the fall especially deer can be very violent. The fall is their mating season. Males will fight each other until one dies to win the right to mate with a female.