It's really dumb because it seems like it would be easy to give a reason for why someone whose race was destroyed a raging omnicidal maniac but no, his motivation is that Goku disturbed him with his crying when they were babies I guess.
EDIT
One thing that bothered me about the Broly movie is you have this character that unleashes unparalleled power during berserker rages and it's set during the Cell Saga. Hey you know what other character unleashed unparalleled power during a berserker rage in the Cell Saga? Fucking Gohan! How is this not his story? Like there's this whole deal about how Broly's dad tries to control and limit Broly's power out of fear but then you have Goku who encourages and teaches Gohan to harness his power, so it's like this theme of father/son relationships and contrasting Goku and Gohan with Broly and his father. With that in mind how is the climax of the movie not Gohan seeing Goku about to be killed and then going SSJ2 in anger and desperation for a short period of time wherein he brutalizes and kills Broly and rather than be afraid of Gohan's power like Broly's father was of his, Goku encourages Gohan to use and control his power? It seems like a really obvious thematic parallel.