Just to be clear, Gregory is not actually imprisoned after the fight in question. However, it appears your teacher wants you to imagine that he was, there are several arguments you could use.
The first is that you were simply defending the Capulet name. As a loyal servant of a respected house, defending the family name would have been a positive thing.
Second, you could argue that the Montagues started the fight, and that you were simply acting in defense. In reality, your buddy Sampson bit his thumb at the Montagues, which is the Shakespearean equivalent of giving the middle finger. This no doubt provoked the Montagues. However, you could argue that the Montagues started the physical fighting when they responded to the initial thumb biting.
If you really wanted to save yourself, and if you were willing to throw Sampson under the bus, you could argue that it was Sampson who was the true aggressor. After all, you were simply going to frown at the Montagues, but Sampson heightened the insult by thumb-biting. You could argue that you simply got pulled into a fight based on the impulsive actions of your companion, Sampson.
The entire fight appears in Act 1, Scene 1, so it might be worth a revisit. Hopefully, this gave you a jumping off point for some ideas.