This goes back a lot longer than you could explain with any current connections. It is definitely not connected with any relation to fighting, which is traditionally connected to hard liquor, or to alcoholism, which is often connected to cheap wine.
My suspicion is that in the English speaking world this goes back to the Norman Conquest in 1066. The Normans, who spoke French and drank wine, became the aristocracy of England. The common people spoke English and drank ale. This trend was accentuated by the fact that wine was always imported and more expensive than the locally produced ales. Perhaps this would have worn off in time, especially as wine began to be made in America and Australia; but another factor weighed in. After the French Revolution, the personal chefs of the nobility were unemployed, and some of them began public restaurants. This is when and where the modern restaurant took shape, with some chefs moving to prosperous London and cooking at the gentlemen's clubs and opening restaurants. French cooking became the classic standard for restaurants and for the upper classes of England, and along with it wine reigned supreme.
But the time of beer may be at hand! Thousands of brewers across the USA are producing great beers and their fans are demanding them in the now vast array of types of restaurants. Expensive, classy beers are appearing in upscale supermarkets. Let's see if your question makes sense in a few years, or seems quaint and archaic.

When many people think of beer, they think of sports....many activities of which are violent or aggressive to say the least.

When people think of wine, it's usually related to fine dining and five star or other high end restaurants, dancing, valentines day....getting "in the mood", celebrations and the like. Wine is advertised in a lot of luxury magazines while beer is advertised during the Super Bowl.

Both beverages can be consumed by most adults but they each have a different group or demographic that they appeal too. People who drink wine are likely to be professionals who enjoy a nice night out on the town to relax while many people who drink beer are likely to be found in bar fights or quarrels at rock concerts and sports stadiums. Fighting is not sophisticated. It is disgusting and so the way that these two beverages are marketed and consumed plays a part in their reputation.

"wine has wisdom, beer has freedom and water has bacteria" Ben Franklin
i am no expert on the subject but i believe wine was arround longer, is used in religiouse practices and costs more. beer is relitively cheap and readily available where as a good wine is not and you get to drink it out of pretty glasses. also people tend to drink wine socially and in small quantities where beer drinkers tend to drink more and not for calebratory purposes but in everyday setting.

I've often considered this question as it relates to weed vs alcohol. And beyond the obvious legal stumbling block, I think the answer is the same. Its stereotype. Beer carries the alcoholic image with it more. Although I'm sure wine has its fair share. Maybe a lot of it has to do with the production process. Beer probably seems like a cruder process than wine, which is a slow tedious process.