I don't own TVD wish i did but i don't. Sorry if there's any mistakes I don't have spell check so sorry.
Damon didn't hate Stefan for turning him 145 years ago. He didn't hate him for trying to leave thinking that him and Elena would hook up once he left. He also didn't hate him for giving up his freedom and his girlfriend to get the cure to save him. He didn't hate him because he would do the same thing. Stefan's his baby brother and he would do anything for his brother. Which includes chasing his butt down and dragging him back home were he belongs were Damon could protect him.
Stefan knew his brother didn't hate him. He knew he had forgiven him along time ago. He also knew Damon thought he tried ro be a saint and would risk his life for anyone.
But what his big brother didn't know was that he would not do that for just anybody only him. Cause his big brother was special had followed him for 145 years to make sure he was alright and to protect him even thought he was supposed to hate him.
He knew it wasn't his fault that the warewolf had attacked him. He also knew it wasn't his fault his brother had risked his life for him. He also knew he was not just about to let set back and let his little brother go with Klaus. After all what kind of brother would he be if he didn't go after his Saint of a little brother.
Stefan knew Damon would follow him he also knew if he found him he would leave with him and he didn't care because at the end of the day his big brother would find him. He also knew that when it was all over he would do anything for Damon. Cause thats what brothers are for.