Yes, Insults can easily hurt you, although it really depends on who and what the person is saying
For me i try to ignore the stupid ones like " Your gay" and "you look like a girl" (which is a compliment in my book)
But if it takes me back to a point I dont want to remember, then yeah it will hurt and i might hurt you
Whoever says "Sticks and stones may break my bones but words will never hurt me" has never experienced true emotional pain