The route/highway argument is similar to the pop/soda argument because it stems from a difference in regional dialects, but it's a bit more nuanced. It's less of an argument than a semantic difference.
On parts of the East Coast, people call highways "routes," but only in a specific context. They might call it "Route 495," but then they will refer to "Route 495" as a "highway" when saying something like, "I live just a few miles from the highway." Thus, unlike the pop/soda argument, the East Coasters agree with the West Coasters on what the thing itself should be called—"highway." It's just that when some East Coasters refer to one of these highways by its number, they say "Route ___."
See also the logic behind road numbers.