Of the people I've met who don't drink by choice (as opposed to e.g. allergies or nasty interactions with medication), the most common reason is that they don't feel comfortable with artificially lowered inhibitions. This may not be entirely fair, but I tend to parse that as indicative of a worrying lack of confidence in oneself, either basic or by way of compensating for having had too little self-control in the past. Both are bad news, though not necessarily a deal-breaker in a friendship.

(Other common reasons: previous bouts of alcoholism [also indicative of impulse control problems], prefers other intoxicants [perfectly legit], doesn't like the taste [acceptable in a young person, otherwise usually indicative of a sheltered existence].)