Why should you respect?

Answer 1

you should respect because being respectful is a manner. And if you don't respect anyone you wont get the same lack of respect back. So you need to treat people the way you want to be treated.

Answer 2

People in positions of authority are given these based on their past performance, skills, knowledge and experience (or some combination of these). Showing respect to these people is often regarded as a sign of maturity and acceptance or responsibility, but it also shows agreement with the structure and purpose of the organization of which the person is a member.

Disagreeing with the purpose of the organization does not need to be shown with disrespect, it can be demonstrated verbally (i.e. "I disagree with you and do not respect what you stand for.") or in writing by adopting an opposing position and making your opinions known.

Another participant in this answer wrote:

To give them a good impression about you.