Here's my honest and likely unpopular opinion, but you were a douche. You were talking to the guy like you owned him, I wonder how your clients treat you. What happens if you tell a client you can't take care of SEO for him anymore? Would he be allowed to yell at you and call you a liar?
From my perspective, you're using his service at your own will and if you're not satisfied you're free to go elsewhere and find yourself another doctor. He seems like a decent guy and if he doesn't want to be your doctor anymore, then so be it, he doesn't owe you anything.
If this was in SEO world, let's say you were the "doctor" and you told your client to stop building spammy links and focus on quality content only, because you'll do all the SEO. He comes next month and tells you he still built few millions comment links. You try to explain to him that this is a Churn&Burn strategy and it's not long-term as you discussed from the beginning. You keep telling him that you can't properly do SEO and his site will get penalized if he continues to ignore your advice, but he doesn't even want to listen. At this point, you can't guarantee any safe rankings for his business, as you discussed and you try to convince him that either he stops building spammy links or you won't be able to do SEO for him because the site we'll get penalized sooner or later. He starts yelling it you and calls you a liar because he had heard you also use tons of comment links on your websites, you don't want to see him ranked, that's it... right?
When the whole discussion is over, he goes to his friends and tells him what a jerk and a liar you are because you're using spammy links too, but you don't allow him to do it too. So, who's the jerk?
IMO, you don't have the knowledge and right to give medical advice, that's why you shouldn't argue with your doctor. Even if you're right and he is fat, that doesn't mean what he said is less true.
