1 He was a perfectionist
Jobs was a perfectionist who wanted everything to be done perfectly right. Whenever people didn't stand up to his very high standards he used to fire them in order to replace them with people who have the same standards.
2 He only wanted people who believed in his vision the way he did
Jobs used to fire people who didn't seem to believe much in his vision. He only wanted to keep the people who believed everything he said. If a person challenged Job's future plans he was more likely to fire him.
3 He had very high quality standards
Jobs had extremely high quality standards and he expected all of his employees to share his passion for quality. People who didn't adhere to his high quality standards usually got fired.
4 Success of apple was a matter of life and death for him
Steve Jobs wanted apple to leave a big impact on the universe at any cost. Whenever he felt that someone might slow down apple or prevent it from achieving its important goals he quickly fired him. (See How did Steve Jobs start the Apple company?)
5 He had low patience and tolerance
Steve jobs had low patience and tolerance. He would easily lose temper and burst in anger. This is why he used to fire people randomly without previous planning. Its believed that he used to fire people after meeting them for seconds in the elevator.
6 He wanted only people who believed that nothing is impossible
Jobs only wanted to keep employees who believed that everything is possible. He used to fire the ones who believed that he was demanding too much and that Apple couldn't achieve the goals he has set. (See Why was Steve Jobs so persuasive?)
7 He understood the importance of having the right people
Jobs understood that when the right people are put together they can achieve any goal. Because of that belief he used to fire anyone who didn't seem like he can help the team achieve its goals.
8 He had an insensitive side
Jobs was sometimes very sensitive but in other times, especially when he fired employees, he was very insensitive. This insensitive side made it easier for him to fire people.