Why do archaeologist use tiny paint brushes?

Because a backhoe would damage the stuff they're trying to dig up.

Archaeologists use a number of tools. If they think the surface layer is thick, they might actually use a backhoe, but more generally they'll use shovels and picks to remove the surface layers. When they get down to the interesting layers, they will switch to smaller spades, or trowels. To remove the dirt without damaging the artifact, they'll use brushes, and smaller brushes, and finally tiny brushes to dislodge the dirt.

The key point is, they don't want to damage the artifact.