Why was Haman filled with rage against Mordecai?

Answer: He would not bow down to Haman

The king commanded all at the gate to bow to Haman, but Mordecai would not bow down or pay him homage.

“All the royal servants at the king’s gate bowed down and paid homage to Haman, because the king had commanded that this be done for him. But Mordecai would not bow down or pay homage.”— Esther 3:2 (BSB)