What is the motivation and the purpose for ridiculing someone or something?

when someone i like laughs at me it is a realtionship killer.

To fit in, be part of a group. Also, ridiculing someone else automatically makes you assume you’re better, boosting your ego and confidence, and helping dispel any personal insecurities on that or a number of related topics.

If I focus on your faults, I don’t have to address my own.

When one has low self esteem they ridicule others. That way they themselves look better.

Their self esteem is so low, they want to make you feel bad to make up for it. I put up with it for my entire 13 years in school including kindergarden

to make someone feel better about themselves, or their situation by using words to push another (emotionally) below or under them, giving them a feeling of superiority.

Think of it as an attack. Now why would you attack somebody? All of the same basic reasons apply.
Fear, dominance, pride, social standing etc, etc.

There is one use of ridicule that falls outside of this but is related. It is used in argument to point out absurdities in the other person’s line of reasoning. This is still attack, but it is different than a simple emotionally related attack.

To give yourself a higher sense of yourself. In other words to make yourself feel superior.

Envy of someones personality, not everyone does it.

You seem to be forgetting, Some people can just be really really annoying.