Well, it's an animal, so I would say it is "meat" in the technical sense. It's an organism in the Animal Kingdom, but it's not a mammal like most meat -- but birds (namely chicken and turkey) aren't mammals either.
However, many religions don't classify fish the same as meat from cows, pigs, chickens, or other animals because fish are "of the ocean" and not "of the land" (which could make sense if you put yourself in the mindset of someone 3000 years ago). So it has a religious difference.
Fish also have a dietary difference in that fish is has much less saturated fat and cholesterol than "land meat." So many diets approve of and encourage eating fish because it has protein and unsaturated (healthier) fat, so it might have a different dietary classification too.
And lastly, some vegetarians allow themselves to eat fish because fish is raised differently. Vegetarians often think the treatment of "farm" animals is cruel, so they won't eat it. But lots of fish is caught from the sea/ocean, so it's closer to being "free-range" -- however, some fish are raised in massive numbers in tanks or "farms," but I believe only some fish like tuna or something can be raised this way and most fish is caught from a "free-range" environment.
Bottom Line: You are probably thinking like me that fish is an organism that moves, eats, has blood, etc. Your friends probably believe one of the reasons I stated above (whether they are vegetarians or strict dieters or whatever)