I have a Craftsman mower 917.377795 and will go forward, but locks up on the rear wheels when trying to pull it backwards.

I am not sure I fully understnd your situation. Are you trying to pull the mower backwards or drive it backwards? Is it in neutral when you try to pull?

The Crafsman mower that I have (917.377795) is a rear wheel drive, walk behind. I'm trying to pull the mower backwards while it is neutral (like being under a tree), but the wheels lock up in doing so. I'm new to this website, so I hope this information gets to all of you who sent me a message, thank you!

Sounds like the pinion gears on the drive shaft are rusted of full of debri.
Also could be clutch cable not releasing ,
Luck