Question

Why do iago, roderigo and brabantio hate the man they are discussing?

Answer 1

In the opening scene, each of the character Lago, Rodrigo, and  Brabantio had different issues with Otello, however, the only character you used the word hate, was Lago.

Brabantio was angry and hated Otello because he believed Otello had bewitched and used voodoo on his daughter, for her to have eloped with him.

Rodrigo hated Otello because Otello had taken the girl he wanted to marry (Desdemona).

Lago, on the other hand, hated Otello because Othello made Cassio 2nd in command instead of him. He feels Cassio was less experienced.