Why do my dwarves climb trees?

Climbing trees is meant to be a feature if your dwarfs can't get to their objective any other way. However, their aggressiveness in climbing up a tree and refusing to come down is a known bug. Often changing their labors around temporarily, or temporarily giving another dwarf the job they refuse to do, is enough to snap them back to reality. Sometimes they're stuck up there forever. This is DWARF FORTRESS!

Its a feature. On the wiki it says:

Trees can be climbed in both fortress and adventurer mode. In densely wooded areas, the overlapping tree crowns can form a continuous canopy that can be traversed by walking, climbing and/or jumping. Both types of branches provide floor-like support for walking, but twigs are too frail to support the weight of a dwarf. All kinds of trunk tiles are treated as solid barriers, except trunk tips - they can be walked and jumped over.

I couldn't find any source where this is concerned as an issue so its not really a problem.

In adventurer mode you can climb them yourself by pressing H to first hold on it and then moving by pressing the movement keys, but I guess you already figured out.

"tree" on dwarf fortress wiki