Final Fantasy 7's late-game segments confirm Cloud hates Sephiroth because he is a reminder of his failure and weakness, which nearly cost Tifa's life, the person who motived him to join SOLDIER in the first place.

Why is cloud traumatized Sephiroth?

He eventually leads the party to finally defeat Sephiroth. Cloud suffers a form of PTSD from his trauma after the death of Zack. But that was not the only trauma he went through — his mother was killed by Sephiroth when he was 16. ... And then he almost died because that person tried to kill him.

What happened between Cloud and Sephiroth?

Cloud moved Tifa to safety, then the battle continued. During the fight, Sephiroth skewered Cloud with his sword, Masamune, but Cloud fought back. Using Masamune as a level, Cloud flung Sephiroth into the Lifestream below the reactor, presumably killing him.