Why do some drummers hold sticks differently?
Because of that drum position, using an overhand grip on the high (left) side of the drum would force the elbow into a very awkward position while an underhand grip is much more comfortable. Even when the drum is on a stand, many drummers will tilt their drum when using traditional grip.
How can I improve my drumstick grips?
Curl your other three fingers onto the drum stick, wrapping your ring, little, and middle digits underneath it. Much like with your thumb, these fingers shouldn't grip too tightly. This hold enables advanced control of your drum sticks while letting them bounce back from the drum head.