I think cats climb trees for lots of reasons and I'll list a few here. But I think you know which one of these reasons is the REAL reason cats climb trees...
1. Cats are predators so they want a better view of their surroundings for the attack.
2. Cats can escape animals that might be chasing them.
3. Cats climb trees for fun, you know, sort of like why people climb trees if they aren't arborists.
4. Cats see something in the tree that "caches" their attention (like a bird or a squirrel) and just can't resist checking it out.