How and Why tybalt provokes mercutio?

Both are character foils for each other. At the very least they are rival "tough guys". Tybalt is serious and Mercutio uses humour to get under Tybalt's skin. Check out this exchange between the two,

TYBALT

Follow me close, for I will speak to them.

Gentlemen, good den: a word with one of you.

MERCUTIO

And but one word with one of us? couple it with

something; make it a word and a blow.

TYBALT

You shall find me apt enough to that, sir, an you

will give me occasion.

MERCUTIO

Could you not take some occasion without giving?

Mercutio gets under Tybalts skin by being overtly funny with sexual undertones (my interpretation at least). Mercutio isn't exactly a barrel of laughs and takes Mercutio's bait every time.

OOPs, I meant Tybalt isn't a barrel of laughs in the last sentence. Certainly Tybalt threatens Mercutio because it is basically what he does. He is "Prince of Cats" tough guy for the Capulets. Hating Montagues is part of his identity. Mercutio knows exactly how to exploit Tybalt and get him agitated.