why was antonio sad ?

You've made this easy; because you've asked for an exact answer.......... we never know why Antonio is so sad. Even Antonio doesn't know why he's sad. At the play's opening Antonio says; "In sooth, I know not why I am so sad. / It wearies me, you say it wearies you" (1.1.1).

Had you asked for inferences this cold have gone in a few different directions, but we never 'exactly' find out. So the answer is.......... he doesn't know