How do I stay away from people who put me down?

There are 4 kinds of people: Ways to deal with them ( As per Patanjali Yoga Sutra)

Happy people: Be friends with happy people, so you will also be happy

Sad people: Be compassionate with them.

Meritorious people: ( People who do good acts) : Appreciate them, else you become jealous.

Demonic People: ( People who do bad deeds ): Educate and ignore.

Try to educate them ( once, twice or thrice). Despite all your efforts, if you think they are getting onto your nerves, just ignore them.

Save your mind at any cost!

On the other hand, if you look at the positive side,

Negative people bring out the skill in you.

They will teach you the art of patience.

By setting an example they are helping you realize not to become like that.

You will eventually find out creative ways to overcome them.

Looking from a broader perspective, you cannot but feel compassionate for them.