1) I don't have any new and useful phrases to contribute, but I will provide my data point of never really having any problems saying "I don't drink". I guess it depends on the atmosphere though. My interpretation of peoples' responses to that is one of the following:

• I don't really know this guy... I don't want to challenge him... Maybe he has a drinking problem?... Maybe someone he knows died in an accident with a drunk driver?... I don't want to offend him.
• Whatever. I don't care.
• Eh, he's probably lame and not fun. Forget him.
• But it'd be so much more fun if you drank with us. It feels good when everyone in the group is doing it together.
• [Someone who knows me] Adam, I want to see how you respond to alcohol.

Responses 3 and 4 seem more rare.

3) My thoughts (which aren't particularly new or insightful):

• The social lubricating aspect of it is big. Disinhibition -> fun. And the environments around alcohol further this as well (dark, noisy, crowded...). I don't get the sense that people consciously reason this way, but I think that they've subconsciously associated it with fun.
• Convention is very powerful. (I realized that you might be asking where the convention comes from, but I still thought this was worth mentioning)
• There isn't really that much for adults to do at night. Well, I mean there is, but other people don't seem to think so. It seems to be (somewhat) frowned upon to stay at home and watch tv, a movie, play games. In other words, people seem to think that you need to go out. Which at night time, pretty much means eating, drinking, or maybe some sort of performance.
• A relevant read - http://waitbutwhy.com/2014/05/secretly-hate-bars.html