There's a few factors that can lead to this problem and range from tool and crank material quality to user error.
If you have a tool made from a weak metal or is manufactured badly (ie diameter is wrong), the threads on the tool can easily be ripped off. Similarly, if the cranks are made from a weak metal, then the threads on the arm can strip off.
User errors can include not moving the inner part of the tool out enough so you end up tighting the outer part of the tool onto the cranks only half way. So when you start winding the puller to press into the bottom bracket, the threads strip.
Another issue could be if someone glued the crank onto the bottom bracket in the past. I don't know if you got the bike second hand or if someone put loctite or glue at some point. But it's possible.
If it's been glued on, you might have to cut the crank off to get the bottom bracket out. Either way, if the threads are gone. I would personally start thinking about replacing the crankset too when the bottom bracket fails, or before if you don't want to risl walking home at some point.
If you're not sure about what to do next, post another question or visit your local bike shop.