Why do we think we need to be respected?

Is respect a need or a want?

What would happen if it does not matter to us whether others respect us or not?

As a Sufi Fakir said, "If you need respect, do not come to me. A shopkeeper or anybody else who wants something from you will give you respect. Goto them."

Consider behaviour of a small child, say a two year old girl. Neither she wants to be respected (she is hardly bothered). Nor she respects others. Her behaviour is kind one moment, rude another, loving one moment, hating another and so on. She lets her feelings rule (and not some societal notion of respecting others or asking for respect)

She is free of respect. She is free of any concept of self esteem.

If you want to argue that as we grow up - we need respect - then you are arguing for your own limitation. If you like it, keep it. If you think it is unnecessary, you can discard it right away!