Why did Jason kill in Friday the 13th?

Answer 1

To avenge the killing of his mother! You need to watch the 1980 version to get the true meaning and back-story of the Friday the 13th franchise.

His mother did the killing in the original Friday the 13th to teach the camp counsellor's a lesson, because years before, Jason had been teased by other kids as he was horribly disfigured and he had fallen into the lake off of the jetty and the counsellor's who were meant to be watching, were just chilling out and ignoring his cries & he tragically died.

So his mom/mum came back to Camp Crystal Lake, some years later to kill a new breed of counsellor's. She gets beheaded at the end of the 1st film by one gutsy girl, who is shown in a boat on the lake the morning after and all of a sudden she is pulled in by Jason.

For the subsequent movies, it is said that Jason witnessed the beheading of his mother and they are of him wreaking havoc and killing anyone who dares set foot in his sanctuary that is Camp Crystal Lake to avenge the loss of his mother.

I recommend Parts 1 & 2 for the story purpose, but thereafter it is just Jason picking off trespassers in the other 7 movies really. Jason X is pretty good too, for a modern revamp of the Jason character.