There are several conflicts between Telemachus and the suitors; they relate to ethics, economics, emotions, and psychology. The suitors want to marry Penelope (well, for her to marry one of them). This would make one of them Telemachus' new father, and would mean he gave Odysseus up for dead. He doesn't want that. He wants to be a good son, and loyal. At the same time, the Greeks put a high value on hospitality—but the suitors were eating everything in sight. He wants to spend less feeding them, for them to go away, and for them not to threaten his mother; they want to eat, marry his mother, and replace his father.
As to how I'd respond, probably not as well as he did. I suspect I would have either run away or cracked long before and attacked one of them.