Is it fair for my boyfriend to ask me to stop drinking?

My boyfriend has recently been suffering from health problems. I have been trying to support him as best as I can, but I can't give him one thing he keeps requesting and claiming will support him; to cut alcohol out of my life. I do not have a drinking problem, abuse alcohol in any way, or suffer extreme personality changes when drinking. I have offered to not drink around him, but that is not good enough. He claims that he can deal with being around people who are drinking, just doesn't want to see his girlfriend drinking. These requests have all stemmed out of his health issues. He is not a controlling person, but I can't help but find this request to be unsettling. I do not have any desire to give up the occasional drinks with my friends, or the option of going out with friends to unwind over cocktails. Am I being stubborn, or is his request just too far out there?