In Othello, what are Roderigo's and Iago's feelings towards Othello?
Iago and Roderigo both despise Othello but it is Iago who has an irrational desire to ruin Othello. Roderigo's hatred is based on Roderigo's own apparent 'love' for Desdemona. He is so foolish that he thinks that Desdemona can be his if only Othello is out of the picture.
Roderigo is Iago's pawn, doing his bidding and even paying Iago to secure his favor with Desdemona. He allows Iago to manipulate him and even when he realizes that Iago has only his own interests at heart, "I do not find that thou deal'st justly with me" and he has "wasted myself out of my means" he is still persuaded to act to secure his love interest.
The hatred Iago has for Othello is immeasurable and, in some instances, unfounded. He is paranoid and believes Othello may have even
leap'd into my seat; the thought whereof
Doth (like a poisonous mineral) gnaw my inwards
He has no reason to think this and even Emilia tells him it's absurd.
The fact that Cassio was promoted sets Iago off on his path to destroy Othello as he cannot believe that there is any sensible reason why Cassio would have been promoted over him, an experienced soldier.
Revenge is the main motivator for Iago and all his actions come together so that it appears that he is not the only instigator, having most of his compatriots believing he is "honest" Iago.
It is perhaps the similarities between Iago and Othello that push Iago to destroy Othello and all those connected to him
Iago is the only character who speaks directly to Othello's sense of his own inadequacy.
Iago almost relishes his devilment, "I am a very villain else" and his feelings towards Othello do not falter. Each occurrence serves to strengthen his resolve and with Roderigo as his willing co-conspiritor, he cannot be stopped.