Yesterday I saw Captain America: Civil War. Captain America, Black Panther and Zemo had a conversation on the mountain. Zemo said he was sorry to have killed Black Panther's father. Then why did Black Panther not kill Zemo?
Because T'Challa no longer believes that revenge is a good reason to take someone's life.
Let's look at it from T'Challa's perspective at the point in the film when he decides that revenge isn't worth it. He's sitting next to the man who has killed multiple innocent people in his quest for revenge, after just learning that the man he was trying to kill (Bucky) is actually innocent of the crime he was trying to kill him for.
Meanwhile, two people who used to be good friends are beating each other half to death thanks to the fact that Tony wants to get revenge on Bucky.
T'Challa has seen how revenge isn't worth the risks that come with it. He's seen how it makes people irrational, how it can tear people apart, how it can turn otherwise good men evil, and as such decides to arrest Zemo instead.
In short, he's now above getting revenge. In his own words (or at least, what I think his own words are);
Vengeance has consumed you. It is consuming them. I'm done letting it consume me.