Reviews for "Captain America: Civil War" revealed that Black Panther has a personal vendetta against Bucky Barnes. T'Challa is out to get his revenge on Barnes for what he did to his family.
Barnes is in a lot of trouble in "Captain America: Civil War," not only from the government but also from Black Panther. According to Moviepilot, T'Challa hunts down Barnes because he murdered his family. It is not exactly clear how Barnes, as the Winter Soldier, killed Black Panther's family. However, it is said that Cap's best friend committed a heinous crime against his family.
This crime is described as a vicious attack, so it seemed the bomb attack that implicated the Winter Soldier (Sebastian Stan) caused the death of Black Panther's family. The terrorist attack may have taken place in T'Challa's home country in Wakanda. The bomb was aimed at the royal family, who so happened to be Black Panther's family.
Additionally, the video below shows T'Challa grieving at the rubble following the explosion. This scene only further proved the bomb attack is what killed his family. This would explain why Black Panther (Chadwick Boseman) hates the Winter Soldier so much and why he decides to side with Iron Man in the movie.
In "Captain America: Civil War" Black Panther also sides with the Sokovia Accords. He has his own agenda for agreeing to the mandate. He not only wants to see the Avengers' missions controlled by the government, but he also wants justice for what happened during Team Cap's tragic mission.
This mission, according to reports, happened in an African market. Captain America, Scarlet Witch, and Falcon, are sent to stop a deadly explosion from happening. Brock Rumlow aka Crossbones seemed to be behind the attack. However, things do not turn out according to plan, when an explosion is triggered instead. According to Entertainment Weekly, Scarlet Witch is somehow to blame for the blast, since she is after all, still adjusting to her powers.
The explosion caused the deaths of many civilians. This catastrophic event eventually led to the United Nations passing the Sokovia Accords. Black Panther is taken in as member of the committee that oversees the accords, because of his connection to the tragedy.
See Black Panther hunt down Bucky Barnes in the video below.