Both words are pronounced exactly the same way, but they are completely different in meaning.

“Incite” means to encourage someone to do or feel something unpleasant or violent.  When you incite people, you are goading them into an action which will cause harm to themselves or to others.

Below are some examples using “incite”.

• The noted politician incited his followers to burn cars and beat up people, to protest against the government. 
• Brenda was expelled from school for inciting her classmates to rebel against their teachers. 
• The local leader incites hatred for coloured people through his speeches. 
• David incited his sister to splash the white walls with green paint. 
• The workers were incited by the union leader to go on strike. 
• Hitler incited an entire nation to wipe out the Jews. 
• The propaganda unleashed online by religious groups incites young children to join their ranks and kill innocent people. 
• The promise of reaching heaven is what incites people to commit suicide and kill thousands of people. 
• A man was inciting his girlfriend to commit suicide because they could not get married. 
• James was incited by his wife to turn against his parents. 
• The news of a tsunami incited widespread terror and panic. 
• Rose incited her husband to steal a necklace for her. 
• Some drugs incite users to become violent and dangerous. 
• Cinema can incite people to try out stunts which are dangerous. 

From the above examples it is clear that it is not very nice to incite someone to do something bad.  On the other hand one can “entice” a person to do a task by offering rewards.  See the sentence “The band of thieves incited an innocent bystander to join them by enticing him with money”.

The word  “insight” is a noun which means the ability to gain an accurate and deep understanding of something or someone; or, the ability to understand people and situations in a very clear way.  Examples are given below:

• As we get older we get a better insight into situations that we did not understand in the past.  (We get a better understanding of situations.) 
• Churchill was a leader of great insight which helped him win the Second World War.  (Churchill was a leader who understood Hitler’s mind.) 
• The book offers a rare insight into the North Korean regime, which was up to now little known.  (The book offers a deep understanding of the North Korean regime.) 
• The police officer excelled in handling hardened criminals.  He had a rare insight into the causes of their behaviour.  (The police officer understood the mind and behaviour patterns of criminals.) 
• Psycho-analysts have an insight into the minds of their patients.  (Psycho-analysts understand the minds of their patients.) 
• The book offers an insightful description of daily life in a concentration camp.  (The book offers a deep understanding of life in a concentration camp.) 
• The mechanic should be like a doctor and have an insight into what has actually gone wrong with car.  (The mechanic should understand the machinery of a car to pinpoint a problem.) 
• A start-up company should have an insight of where it will be ten years hence.  (A start-up company should understand where it will be after ten years.) 
• The match was won because the captain of the winning team had an insight into the strategies of the opposing team.  (The match was won because the captain of the winning team understood the opposing team’s strategies.) 

To sum up “incite” is a verb while “insight” is a noun, and neither has a relationship with the other.

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