In Othello, why do Iago, Roderigo and Brabantio hate the man they are discussing in Act 1, scene i?
Each of these characters has a specific situation to deal with in the play as revealed in the opening scene, and these situations drive their opinions about Othello:
- Iago, it appears, feels slighted at being passed over for a promotion by Othello, it could be that a sort of revenge is driving his hatred;
- Roderigo potentially hates Othello, because he has "stolen" the girl that Roderigo wanted to marry -- Desdemona;
- Brabantio potentially hates Othello, because he believes that Othello bewitched his daughter to make her run off and elope with him.
However, the only character who comes straight out and uses the word "hate" is Iago. Since he is the villain of the play, it is important that his bad feelings seem larger and more destructive than other characters. He mentions his hate quite a few times, and Roderigo even begins the scene (and the play) with the line: "Thou told'st me, thou did'st hold him in thy hate." So, if you believe what Iago says, then he hates Othello.
The thing that makes Roderigo appear to hate Othello (and he might, in fact, hate Othello; it just isn't stated blatantly in this opening scene) is that he refers to him with racial slurs. He calls Othello "thicklips" and "a lascivious Moor." Referring to Othello by his lips and his heritage rather than as his individual self is a bigoted thing to do, but cannot confirm that he hates Othello.
As for Brabantio, we know from Othello's speech later in the Act that he had often been Othello's kind host, that, in fact, Brabantio's home is where Othello and Desdemona met and fell in love. But he also refers to Othello as simply "Moor" and assumes that Othello has used some voodoo to bewitch his daughter to marry him. Again, a bigoted point of view, but not proof of hatred.
If you are looking for proof in Act I, scene i of hatred towards Othello, you will only find direct textual confirmation of this in the lines of Iago, the other feelings can only be inferred.
We discover in this scene that Iago has outright stated his hatred for Othello, as Roderigo recounts, "Thou told'st me thou didst hold him in thy hate." Iago acknowledges this, and even explains why he hates Othello so much. In Iago's mind, he is "worth no worse a place" than that of Othello's lieutenant, but Othello has rejected his suit and instead chosen Michael Cassio, a man who has "never set a squadron in the field" and is, Iago feels, far too inexperienced for the position. This slight against Iago is what initially drives his move against Othello. Later in the play, he states more than once that he feels Othello may have slept with his (Iago's) wife, but he does not mention this in Act I, Scene I.
Roderigo does not state any hatred of his own for Othello, although his response to Iago's complaints suggests that he thinks they are justified—"I would not follow him then"—and the language he uses to describe Othello is derogatory ("the thicklips"). Later in this scene, we find out that Roderigo may have his own motives for helping Iago reveal to Brabantio Othello's new marriage. Brabantio declares that Roderigo has "heard me say / my daughter is not for thee," and the audience may interpret that Roderigo had pursued Desdemona. Instead, Desdemona has chosen Othello for her husband.
Meanwhile, Iago attempts to rouse Brabantio's ire against Othello through the use of coarse language, stating, "an old black ram is topping your white ewe." Brabantio does not express hatred for Othello directly, but we know he is unhappy about the match, declaring it "too true an evil" and stipulating that he would rather Roderigo "had had her" after all. Given that we see no real reason for Brabantio to dislike the Moor and that he seems to have been roused by Iago's racist language, we may infer that Brabantio disapproves of a marriage between his white daughter and the black Othello.