Similar to the the pop/soda argument, because it stems from a difference in regional dialects, but 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 calledââ¬â"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.