There is a common acceptance among the fanbase (at least in the western fandom) that it was Son Goku’s crying as the source for Broly’s insanity and/or hatred. Yet, upon rewatching the film numerous times—this doesn’t seem to be the case.
Let’s start with the premise of the discussion:
Does Broly hate Goku solely because he cried? Let’s examine what the film,
Burn Up!! A Red-Hot, Raging, Super-Fierce Fight!, says regarding their relationship first. Does Broly even
remember Goku in the first place?
Goku first appears to Vegeta, Paragus and Broly at
20:22 mark; as Broly is within earshot, Vegeta refers to Goku by his Saiyan name during their exchange. There was immediate tension between Broly and Goku before Paragus activated the mind control device to calm Broly down.
Paragus immediately had his mind control device checked out by the engineer, only to be told that it was working in perfect condition. Not satisfied with the results, he began to ponder what was truly making Broly act out. Thus, we’re prompted with Paragus’ speculation:
Paragus: Could it be Kakarot...? Does this mean that Broly’s instincts as a Saiyan have been awakened by Kakarot’s power and he is starting to overcome the limits of my control?
Paragus speculates that Broly reacted not to Goku entirely, but rather his power, and starts to fight off the mechanics of the mind-control to stimulate his instincts as a Saiyan. This is supported when Broly promptly attacks Goku at night starting at 26:25.
Prior to their short battle, Paragus dabbles on the history of Broly and reveals that because of his extraordinary power, he became more savage as he grew older:
Paragus: Broly was the very model of a Saiyan. As he began to develop, the extraordinary battle power he was born with increased and turned savage to the same extent as I, his father, felt terror towards him.
Throughout the film, from Paragus’ analysis and Broly’s behavior, nothing indicates that Broly even remembers Goku nor knew his name prior to his meeting in the hallway at 20:22. Instead, we’re given other explanations for Broly’s behavior.
The closet confirmation regarding Broly remembering Goku is from Mr. Takao Koyama, a screenwriter behind majority of the Dragon Ball Z films. Upon answering various questions, he was prompted with this one:
Does Broly remember his trauma as a baby as "the only memory of defeat"?
Koyama: That's right. I didn't come up with it alone but decided after discussing it with other staff members. The memory of Broly losing to Kakarot, who is far weaker than himself, remains a traumatic memory. When Broly loses, he remembers when he was a baby. I meant to allude to his trauma (Why does Broly hate Kakarot) in that scene. I want you to judge for yourself whether this was properly conveyed to the viewers.
However, this doesn’t discuss upon their first meeting in that hallway scene—rather touches the ending where Goku defeats Broly. This ties to our next segment:
What was the purpose behind the crying scene? Was Broly always this crazy?
Paragus stated clearly that Broly was always a crazed maniac, and the increase of power as he grew simply added to his barbarity and savagery. The whole purpose behind the mind control device wasn’t to just suppress his power—it was to suppress his sadistic personality. Once Broly’s Saiyan instincts were activated, he managed to break through the device and reveals who’s he is truly: a Saiyan who craves battles and destruction. Considering that both Goku and Broly take elements from Sun Wukong, it is not surprising that Broly had these characteristics of unhinged, battle maniacs with no regard for others. See how he threatened Goku and the others if they do not demonstrate the will to fight, he’ll simply destroy the entire world; praises them for putting up a fight despite being futile and causally destroyed the planet that the slaves were on or the sole purpose of enjoyment.
During Paragus’ flashback, we’re shown Broly and Goku as babies, born on the same day. This is what Paragus states upon remembering such detail:
Paragus: "Broly and Kakarot were born on the same day, one right after the other. If it is Kakarot...", "Damn, the threads of destiny have once again intertwined here, have they? The two infants, born on the same day and laid down in adjoining beds..."
Furthermore, we’re introduced by two characters that comment on Broly and Goku respectively:
"I'm shocked by Paragus' son. He's just been born, and yet his battle power is already 10.000."
"Bardock's son, with a battle power of only 2, made Paragus' son cry! (laughs)"
"His battle power may be low, but that kid who they named Kakarot at least has a lot of guts!"
This is foreshadowing for the conclusion of this film and ties into what Koyama mentioned. Despite the huge gap in power, Goku still managed to affect Broly. This is showcase again when Broly practically dominated the battle, only for Goku to stand up once more and promptly defeated him (making him a two-time loser). Regardless of whoever the opponent is, Goku still stands and fights—because he has lots of guts. Paragus’ words, referring to their meeting as a matter of destiny and intertwined fate, gain a new meaning: Broly’s defeat by Goku was guaranteed.
You can see Broly’s reaction after Goku gains power from his friends:
Broly: W-what kind of guy is this?!
Goku: I ain’t letting you get away with this!
Broly sweats, starts laughing: “No matter how much power you absorb from those small fries, you cannot overcome me!
Goku: We’ll see… You never know until you try!
From that point, we can establish that Broly’s hatred for Goku began upon his defeat, twice now. Which trails over to the 10th film of the franchise—where Broly’s sole purpose is to defeat Goku. And Goten’s cry causing that bad memory of being defeated twice led to Broly’s ongoing hatred to Goku. This was directly stated by Krillin towards the end of the 10th movie:
"For that Broly guy to follow us all the way back to Earth, he must really be upset when he lost to Goku, huh?"
