I see the "agree to disagree" as a bit of a social flag for the conversation that says "I don't wish to get into it / continue arguing about it" because there is no way to respond to it. If you try to continue the debate you look like an asshole, and if you drop it the person who says it gets to continue being wrong without being challenged.
It's very annoying and I hate it.
If the partner is snoring loudly they might have a form of sleep apnea. They should get a sleep study done just to check. My husband's snoring was so loud I could sometimes hear it through earplugs. He had sleep apnea, now he uses a CPAP machine and no more snoring and better sleep for both of us.