In the beginning I also saw Tendou as an arrogant asshole, but then later on, I started to understand him a little more.
One of the reasons people dislike him, is in fact because he is completely honest. He will let people know if they are speaking nonsense, and he will tell them exactly what he thinks about them.
The thing is, he was always right. Kagami would never have matured the way he did if it had not been for Tendou. Heck, Kagami would probably have been killed by the worm who mimicked his brother if Tendou had not smacked some sense into him.
Hiyori would never have learned to cook well if he had not been honest and said that some of her cooking tasted horrible. etc etc etc.
I also think that people hate him because of the fact, that he was not afraid to admit his own flaws.
He basically said that "I will follow my own rules, but I am willing to break them myself if they interfere with my own interests".