Broly's power acted as a monster inside of him. In a flashback during the first movie, you can see that Broly attacks his father, injuring his eye. It is the nature of a super saiyan to lose control (the first super saiyan ever destroyed himself upon transforming). You can imagine that a Legendary Super Saiyan would be even more destructive. In the DBZ series, King Kai comments on how Goku is struggling to hold on to who he is when he first became a Super Saiyan.
Because of the above, Broly is very far from being himself when he kills his father. Take note of how he says the line "Where do you think you're going, Dad?". The monster inside Broly couldn't care less who Paragus was, as far as he's concerned, he isn't even his father.
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Duh broly is evil he is the most powerful legendary super saiyan. And the reason he is evil and mad at goku is because when Broly and Goku were both babies they had beds next to each other when they were little babies goku kept crying and disturbed Broly from his sleep. Also if your wondering why Broly is power the doctors in DBZ said he was born with a power level of 10,000 and kept training. After a few days of Paragus (broly's father) and broly's banishment from planet Vegeta, Broly kept getting out of control with rage. And their you have it that is why broly is evil hope this helps also you should just rent the movie on DVD and just watch it to find out the story of Broly
Goku and broly were born on the same day, goku was a loud crybaby and thus cased a restless broly to start crying. 30 so years later Broly never forgave him for it. Because of all that broly hates goku and wants to kill him.
The reason is because broly has so much anger from all the krap he went through with janemba
His name was Paragus.
Ah, what a delightful question. The epic battle between Broly and Goku can be found in the movie "Dragon Ball Super: Broly." It's a beautiful clash of power and determination that will surely inspire your own creative spirit. Just sit back, relax, and enjoy the colorful brushstrokes of their fierce encounter.