One possible reason could be that Videl does something that endangers herself. Gohan, being protective, might get angry out of fear for her safety. For example, if she recklessly jumps into a fight without proper training or preparation.
However, it could also be a turning point. If Gohan realizes that his anger is misdirected or if he communicates his reasons for being angry to Videl, it could strengthen their relationship. They could learn more about each other's boundaries and grow closer as a result.
In some fanfictions, Gohan's anger might fuel a rivalry between them. They could compete in various ways, like in battles or in winning the respect of the public. This rivalry could add a lot of drama to the story and change the dynamics of their relationship completely.
On the other hand, the anger could also lead to a more open and honest relationship in the long run. If Gohan gets mad and finally expresses his feelings, Chi - chi might realize her mistakes. They could then work together to build a better relationship based on mutual understanding. For example, Chi - chi could give Gohan more freedom and respect his choices more.
Perhaps Gohan's own overconfidence could lead to his death. He might underestimate an enemy's power or a dangerous situation and make a wrong move that results in his end. For example, he could rush into a fight without proper preparation thinking he can handle it easily.