I will bite my thumb at them, which is disgrace to them if they bear it. (1.1.44)
Sampson and GregoryThe streets of Verona
I do bite my thumb, sir. (1.1.46)
Do you bite your thumb at us, sir? (1.1.45)
Montagues and Capulets get into a fight. (Hate)
If you ever disturb our streets again, your lives shall pay the forfeit of the peace. (1.1.98-99)
Sampson hates Montagues so much that he does anything he can to anger them and start fights with them.
Act 1 Scene 5
This, by his voice, should be a Montague.-- Fetch me my rapier, boy. (1.5.61-62)
This relates to the motif of hate because biting your thumb is a significant action. Sampson bit his thumb to anger the Montague servants because he hates them and wants to fight them.
Capulet and TybaltCapulet party
'Tis he, that villain Romeo. (1.5.73)
Shakespeare is demonstrating that the only thing that comes out of hate is fighting and arguing. You do not gain anything from hating someone and it just starts problems. You also can have consequences and punishments.
Tybalt is angry that Romeo, a Montague, is at a Capulet party. (Hate)
I will withdraw, but this intrusion shall, now seeming sweet, convert to bitt'rest gall." (1.5.102-103)
Tybalt hates Romeo because he is a Montague and he wants to punish him for showing his face at a Capulet party.
This relates to the motif of hate because Tybalt calls Romeo a villain. He hates Montagues and Romeo angers him.
It is my will, the which if thou respect, show a fair presence and put off these frowns. (1.5.81-82)
Shakespeare is demonstrating that hate makes people angry and if Tybalt had not been stopped by Capulet, a fight could have started and they would be punished. Nothing good comes from hate.