Shylock is an obvious candidate to be the play's antagonist, as he's the dark character who is inarguably on the fringes of the society. He motivates the main conflict in the plot about the debt, and he is immovable on the point of wanting Antonio's flesh rather than monetary compensation. Shylock also openly admits to hating Antonio, as he is a Christian and also bad for business. When Shylock leaves the play, Bassanio's romance with Portia has mostly been sealed, so Shylock was the last meaningful conflict to be resolved. (The ring affair is negligible, as Portia jests before Act V that it will be a fun source of jokes on the men.)
All of Shylock's worst features stand to make him the antagonist, and he is full of antagonism towards those around him. But what complicates the situation is that, unlike many of Shakespeare's other villains (Edmund in King Lear, Iago in Othello, Oliver in As You Like It), there is a perfectly reasonable premise for all of Shylock's hatred. Depending on your interpretation, Shylock can be played as a hate-filled but justified character who inspires compassion, or as the worst stereotype of a stingy, stubborn, cruel, unfeeling money-lending Jew.
With respect to the play's two plots, Antonio is either a loyal and benevolent keeper of his dear friend Bassanio or an utterly deluded anti-Semite. If the play is interpreted as a statement in favor of all mankind's humanity, then both Shylock and Antonio can rightfully be condemned for their religious animosity. But Shylock is in the position of the oppressed, so his hatred is a reaction. Antonio is in the majority and therefore in a position of power. He pursues his hatred of Shylock for no reason other than malice. Antonio's resignation to his fate seems to be an admission of this. As he has been malicious and merciless, he expects Shylock to treat him the same.