Speaking of prisms, one of the aspects of this debate that hasn't been mentioned yet is sporting culture. Americans in general do not like ties. If there is any word in sports that is quintessentially American, it is the word "tiebreaker". Even-steven outcomes of any kind are not a part of our sporting culture. We're indoctrinated at a young age in the absolute importance of winning, and that winning and losing are a clear-cut binary. Our national pastime has what is essentially a play-till-you-drop rule that for the most part eliminates the possibility of ties. (American baseball fans tend to be utterly perplexed when they first learn that ties are allowed in the Japanese major leagues.) Our one homegrown sport that the rest of the world has wholeheartedly embraced, basketball, likewise has a play-till-you-drop rule to ensure a win/loss outcome. Football had ties for many decades, but they were relatively few and far between; it was a novelty if a team had more than one tie in a season, and most seasons a team wouldn't tie at all, whether it was on the high school, college, or pro level. Even that infrequent outcome proved too much for football fans, so the various levels of the sport came up with their own overtime rules to dispel the dreaded draw.
Soccer's closest sister sport on these shores, hockey, has long been subject to ties for the same reason as soccer: it's darned hard to score, and the only scoring increment, a goal, counts for one. That means that if you're behind you must first come level before you take the lead, which, along with the difficulty of scoring, is a surefire recipe for ties. And hockey, like college soccer, has flirted with various tiebreakers, including the alien and bizarre method of shootouts as well as overtimes. That's because the people who love hockey the most, Canadians, share the lack of affinity with ties that we have here south of the border.
But the soccer world south of the Rio Grande and beyond the seas has no such compunction about draws. To the rest of the world, draws are very much a standard part of the game, and, indeed, are often a preferred strategic objective. And I think that there's a divide among American soccer fans between those who like the game and have added it onto their sports-fan menu as one sport to follow among many, and the diehards who have adopted a more exclusive and more global (for lack of a better term) outlook and who thus choose to view the sport through the prism of Europeans, Mexicans, Central and South Americans, Africans, and Asians. To them, acceptance of the draw as a legitimate outcome -- in fact, the insistence upon calling it a "draw" rather than the more American "tie" -- is to them part and parcel of what being a fan of the beautiful game is all about.
I'm going to do something dangerous and say that neither outlook is right or wrong. If you want to be all Yankee Doodle about it and declaim that ties are un-American, that's fine. If you want to be the cosmopolitan soccer purist and insist upon the globally-reinforced mentality that draws are simply a natural part of the sport of futbol, that's fine, too. If you're a mix of those two schools of thought -- hey, no problem with that, either. There's no right or wrong way to be a fan -- unless you're storming the field and inducing the riot police to load up their tear-gas canisters, that is.