Uncivil vs. Incivil

First, I need to acknowledge that civil has a few definitions, and the one I’m focusing on is the one related being courteous and polite. Its origin is Latin, meaning “citizen”.
 
From there, I’d like to focus on the antonyms (opposite meaning) of civil.

• Uncivil – an adjective that means discourteous and impolite – the opposite from what civil means. I would argue that there is no such word as incivil, although I have heard people use it before. But people’s use of a word does not make it proper. Just think of the word 'alright' (correct spelling all right), and you get my point.
  

Example: Margaret was uncivil to Bob at work. She refused to help him get a job done that would benefit the organization. Margaret is known for creating unnecessary conflict.

• Uncivilized – while it is also an alternate adjective used to describe someone as being impolite, it is can be used to describe a place or people who are not considered to be socially, culturally, or morally advanced.

Example: It is common knowledge that Margaret is uncivilized and should perhaps work from home if she can’t work well with others.

• Incivility – the noun version used to describe a rude or impolite attitude or behavior. This might be the source of why some people think incivil is a word, but that’s only my best guess.

Example: Everyone at work now has to take civility training because of Margaret’s incivility.