I think my sister's boyfriend likes me.
Do you like the way he talks to you?
No, I don't. It kinda hurt my feelings when he talked to me so sweetly.
It's wrong to get involved with another person's romantic partner and especially so when that partner is involved with a family member. It can lead to cheating and a lot of emotional hurt and drama. You should firmly turn down the advances from your sister's boyfriend so that he knows it's not acceptable to flirt with others while he's in a relationship.
But in the end I want him to like me, and I want to prove to my sister that he's not perfect for her.
It's great that you have someone you might like, but he belongs to your sister. It's not right to home wreck her relationship, because it will ruin your relationship with your sister, too. You have to think about how she would feel about you and her boyfriend doing this to her.