Cloud confessed in the lifestream that the actual reason he served Shinra was to please Tifa. The late-game elements of Final Fantasy 7 indicate that Cloud despises Sephiroth because he reminds him of his failure and weakness, which almost lost Tifa's life, the person who pushed him to join Soldier in the first place. This is further confirmed when you can talk to both characters at the end of the game; if you ask either one about their relationship with Sephiroth, they will say that it is forbidden.
In addition to this, Cloud also admits that he wants to destroy Sephiroth, who destroyed an entire city (Nibelheim) looking for him. Finally, after defeating Sephiroth, you can ask him why he fought so hard and he will say: "I wanted to see your face again." This implies that even though they are both servants of Shinra, they still want to fight each other.
Sephiroth hates Cloud because he believes him to be responsible for the death of Aeris. In order for her to reach peace, Sephiroth destroys Cloud's body, but his soul goes up into space where it meets a spirit called "Free Will". Free Will tells Sephiroth that there is one person on Earth who does not deserve to die and she is not him. She is Tifa, who was supposed to be his friend and partner but ended up being his enemy.
However, this is only suggested by the game, as Sephiroth himself states that he does not understand why everyone hates him.
In the opening scene of the game, when Cloud attacks Sephiroth, he calls him "little man". This could be a reference to how Cloud sees himself as insignificant compared to Sephiroth who has been referred to as "the great hero". Or it could be a term of endearment used between friends. There's also a line in the song "One More Chance" that refers to Cloud as being small enough to fit in Sephiroth's hand.
As for Sephiroth, he calls Cloud "boy" or "child". This could be because they are both just kids who want to save the world or it could be because of their relationship with Tifa. When asked about his real name, Sephiroth replies "it's nothing special", suggesting that he feels like any other person named Sephiroth would think similarly of himself.
Cloud claims that he's seen everything, which might mean that he's seen evil in all forms including those that wear a mask like Sephiroth.
In the original game, Sephiroth isn't concerned with the cloud. Sephiroth uses the Cloud as a means to obtain the Black Materia at one point, but otherwise ignores him. He goes out of his way to murder President Shinra and Aerith, but after he's done, he forgets about Cloud. This implies that Sephiroth is not only capable of ignoring someone, but also capable of forgetting about them.
In Final Fantasy VII: Advent Children, when Cloud meets Sephiroth for the first time in over 10 years, they have a brief conversation about what has happened since their last meeting. During this conversation, it is revealed that Cloud still lives in Midgar and that he has been working as a mover since then. It is also revealed that he has become very strong through training with Tifa and Barret. When asked why he hasn't contacted her before now, he says that she didn't want to get involved with him again. This implies that even though Cloud still lives in Midgar, he has completely removed himself from society and any form of contact with others.
In the final scene of the movie, we see Cloud sitting in a room full of people he doesn't know reading a book. The book is titled "The Seven Wonders", and according to what Cloud reads in the book, it mentions how each of the characters in the story had something remarkable about them.
Sephiroth has had a hatred towards Cloud for a long time, citing Cloud as the only person who has ever genuinely injured him. The issue that Dissidia and KH face is that Sephiroth had other pastimes in FFVII and even AC, such as snatching flower firls from behind, slamming boulders into worlds, or letting children die a slow and horrific death. In fact, he's so obsessed with Cloud that he created a replacement for him called "Ventus".
It's clear that Sephiroth is extremely intelligent and has had plenty of time to think about his hatred for Cloud. He also seems to enjoy causing pain and suffering, which could explain his interest in clouds. Heck, he might even have found a way to control them by now!
In the end, this is just one of many theories that can be made about why Sephiroth hates Cloud so much. What are your thoughts on this topic? Let us know in the comments below!
So Cloud is powerful because he was treated like a solider. But, as we'll see later, he wasn't psychologically prepared for it. The Mako rendered his memory blank, and by the time of FF7, the Jenova cells were beginning to distort his memories in such a way that he would be drawn to Sephiroth and the Reunion. Also, when you consider how much damage the Mako could have done to him, it's obvious that he was given a lot of strength upgrades.
In addition to this, he was trained from a young age to fight to the death, which probably contributed to his current state of mind. Finally, he has been through many battles already, so he is used to killing other people. All in all, Cloud is a perfect fighter who believes he can win no matter what situation he is in, which helps him keep going even when things are looking bad.
Also worth mentioning is his relationship with Aura. When they were children, they were friends first, but as they grew up they started seeing each other from different perspectives. Cloud always wanted to be stronger than everyone else, while Aura wanted to be accepted for who she was. Eventually, they realized they were just trying to fit in wrong and stopped trying to be like everyone else. From then on, they respected and admired each other instead, which is why Cloud can handle himself well against someone like Sephiroth who wants to kill him.