The words incite, insight sound the same but have different meanings and spellings. Why do incite, insight sound the same even though they are completely different words?
The answer is simple: incite, insight are homophones of the English language.
To provoke and urge on: troublemakers who incite riots; inciting workers to strike. See Synonyms at provoke.
The capacity to discern the true nature of a situation; penetration.
The act or outcome of grasping the inward or hidden nature of things or of perceiving in an intuitive manner.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.