It's wordplay. "Have a healthy respect for [something]" means that you recognize that something is important or dangerous, and you give it the respect it deserves. "Bob was a zookeeper. Of course, he was careful whenever he worked with lions or tigers, but after several incidents where ostriches injured his colleagues, he learned to also have a *healthy respect* for ostriches." Here, though, someone believes that authority does NOT automatically deserve respect--they believe that you shouldn't obey automatically, but only after consideration. So, here, they believe that DISrespect is more important than respect. So, they inverted the normal phrase.

Hi Riman " a healthy disrespect for authority" means someone who does not respect authority such as not respecting the government, police or anyone really in authority. People who display this quality will not follow the rules typically and/or will rebel against the rules or any type of authority. This phrase is known as a collocation. Should you wish to learn more collocations or simple develop and improve your English then book a Trial Lesson and I will show you my awesome teaching platform. ( https://teach.italki.com/teacher/7203907) Have a great day!

Criticizing/questioning the rules. As the world advances, some ways of doing things may need to be updated. The phrase, a healthy disrespect for authority, asks that we challenge the rules.

Hello Riman! I think it indicates that the writer feels people in authority - people with some kind of power over others - should not automatically be trusted. Because of this, they do not think people in authority should be respected simply because they have that power. Instead, they think it is sensible (healthy) to not respect someone in authority just because of their position. Hence a disrespect for their authority is healthy... This statement may imply that the disrespect is not total and complete, but instead reserves respect until the person in authority has earned it by, for example, showing themselves to be trustworthy. If they don't earn respect, they don't get it! This phrase also implies that automatically respecting someone simply because they are in a position of authority is an unhealthy thing to do. The writer may, for example, see it as a sign of being brainwashed or of someone not thinking for themselves. I hope that makes sense :-)