I love guys like that. Irritating yes. Change of perspective maybe; you are there to improve you, and he is so willing to correct you...thus, you are there training for you, and he is there training for you... all the focus is on you and not him. lol He gets nothing, you get everything. I smile and nod in those situations... all the focus is on me...even if they are irritating the hell out of me, I remind myself that right now this fool is making the training session only focused on my advancement, not his.
True, you can turn the focus inward onto yourself, and just use him as a tool for your personal training and advancement.
Also, as much as I hate to say it, you can try passive aggressive jabs at him. Anytime he speaks out, you can immediately respond with a comment he would find agravating or insulting. But don't be openly rude about it. A lot of times people can't help being themselves, and they don't even realize they are putting others off by virtue of the things they say. Sometimes putting people in their place can be the eye-opener they needed in order to see the error of their ways.