Used as an insult, usually towards males. Can be used to describe a person who is perceived to compromise goals. Constructed from cock and shite.
Note it is not used to imply dirtiness, nor is it related to sexual organs.
"My brother is such a cockshite!"
"She told me off and I wanted to tell her she was a cockshite."
"You just know some cockshite is going to buy it before you get there."