I've been hugged like that, always a guy....like my chiropractor, who's an awesome guy....that's how he hugs. I don't see anything awkward about it.

My T and I are both female... and she hugs me after every session. They're long and tight, and she rubs my back and reassures me or reminds me to breathe....etc....so she's usually talking during our hug. She usually doesn't let go until I do.