“Hey! The stupid cat climbed up the tree, he can just climb back down.” That is what people say and often that is the case, but not always.
Cats climb trees easily because it is natural for them to do so. Coming down is another story. Coming down is not natural, it is a learned behavior. The cat has to learn how to come down by either watching another cat or by experimenting until they get the hang of backing down the tree. Here is a cool video of a mother cat teaching her kitten how to come down from a tree.
If the cat climbed the tree to escape being eaten by a dog or a coyote, it may stay in the tree several days before making any attempt to come down. If it is tired or hungry, it may just hunker down and give up. A cat can stay in a tree for a long time. The longest I have encountered so far is 14 well documented days.
The real reason you rescue a cat if for the sake of the owner. It is really annoying to hear your cat yowling day and night. Owners sometimes try to climb the tree themselves. This can be very dangerous without the proper equipment. If little children are involved, it can be heart rending. So I delight to do the job. It is an adventure and I make a few bucks too.