Why does Roderigo hate Othello?

Roderigo hates Othello because he has won Desdemona away from him.

In fact, Roderigo has even paid Iago to help him in his pursuit of this woman he loves. In Act I, Scene 1, Roderigo learns from Iago that Desdemona has run away from her home to be with Othello, and he is enraged because Iago has failed him, especially after he has paid him handsomely to assist him in winning Desdemona's love.

....I take...

Roderigo hates Othello because he has won Desdemona away from him.

In fact, Roderigo has even paid Iago to help him in his pursuit of this woman he loves. In Act I, Scene 1, Roderigo learns from Iago that Desdemona has run away from her home to be with Othello, and he is enraged because Iago has failed him, especially after he has paid him handsomely to assist him in winning Desdemona's love.

....I take it much unkindly
That thou, Iago, who hast had my purse
As if the strings were thine, shouldst know of this. (1.1.1-3)

This initial act of treachery by Iago introduces the duplicity of Iago. But, despite this treachery of Iago, the foolish Roderigo is easily enlisted in Iago's plan of revenge against Othello as Iago then assures the gullible Roderigo that he hates Othello, and they should both go to the home of Desdemona's father, Brabantio in order to inform him that Desdemona has left home. Roderigo goes along with Iago perhaps in order to have some satisfaction in enraging Desdemona's father against Othello. Sadly, however, he remains Iago's dupe and is later murdered by this villain.