Tybalt's true breaking point is actually the moment that Mercutio provokes Tybalt out on the street in Act 3, Scene 1. Mercutio had no reason to be out on the street that day. In fact, Benvolio begged Mercutio to leave with him. Benvolio warns that, "The day is hot, the Capulets abroad. / And if we meet, we shall not scape a brawl" (III.i.2-3). Earlier, we learn from Mercutio that Tybalt had sent a letter to Romeo's father, challenging Romeo to a duel. We may be able to assume that Mercutio feels stirred up by the challenge and is out on the streets simply because he wants to pick a fight, which may explain why we do not see Mercutio even attempting to be civil to Tybalt, even though Tybalt is civil to them.
We see Tybalt being civil when he approaches them and respectfully says, "Gentlemen, good den. A word with one of you" (38). In this line, Tybalt uses "gentlemen" to address them respectfully and formally, even wishing them "good evening" in the phrase "good den." We even see Tybalt ask permission to speak with one of them. However, Mercutio returns Tybalt's civil manners with a challenge of his own, "Make it a word and a blow," meaning a "word" and a "blow" from their swords (40). Even though Mercutio further insults Tybalt in this seen, when Tybalt sees Romeo, he is gracious enough to retire from the verbal exchange with Mercutio, because his real quarrel is with Romeo, even saying, "Well, peace be wit you, sir. Here comes my man" (55). However, Mercutio refuses to leave Tybalt alone and challenges Tybalt when Romeo backs away from the fight. Mercutio's provocations finally goad the seemingly patient Tybalt into a fight, which results in Mercutio's death. If Mercutio had not been out on the street and had not challenged Tybalt, both Mercutio, Tybalt, and even Romeo would have continued to live.
Hence, Tybalt's true breaking point takes place during this scene on the street.