To call someone out or to call out to someone is a moderate usage of the phrasal verb call out which means to criticise someone publicly for their wrong doings or behaviour.

1. Yes, Mary is one of my best friends, but I am not biased towards her. Believe me, if she says or does something wrong; I am the first to call her out on it.
2. When Gary wouldn't let me borrow his car, I was quick to call him out on his hypocrisy because I had lent him mine just last week. 

1. Okay, Tom made a mistake, but calling him out on it in front of everyone at the staff meeting was totally unfair.
2. I have reservations about the packaging as I am afraid we might be called out on the sexist colour scheme.