When someone feels jealous of someone else, he might feel like putting him down. People might criticize others just because they are jealous of them.
Some people criticize others to feel good about themselves. The desire to feel better than others can motivate psychologically unbalanced people to criticize others (See why do people strive for superiority).
Sometimes people criticize others because they love them. This is very common with parents. Parents might criticize their children because they love them, and want them to improve.
Some people criticize others because they want them to change to the better. If a person doesn't know how to change someone he will try to criticize him to motivate him to change.
If a person grew up in a home where he was always criticized, he will do the same to people. The voices inside that person's head will keep repeating themselves and as a result he will spit his thoughts out in the form of criticizm.
What people say is a reflection of their own self-perception. If a person always criticizes himself, he will always criticize others. This is the way that this person's mind works.
Mean people criticize others with the goal of making them feel bad about themselves. Mean people know that criticism hurts and so they use it to hurt others.
Sometimes a person would criticize another person just to demonstrate his power.
Some people criticize others to demonstrate their knowledge and to prove that they know more.
Some people accuse others of things they themselves do, in order to deny their own flaws. It's very common for a hypocrite to say that other people are hypocrites. By saying so he prevents himself from ever seeing his own personal flaws.
Most people lack courage. If a person attempts to do something differently, there is a very big possibility that his friends will criticize him and even try to stop him. This usually happens when a person decides to start a business and tells his friends (See staying in the comfort zone).
When a person hates someone he might criticize him in order to release some of the hatred present towards that person (See why some people hate you for no reason).