I will never accept the second floor as being the first floor
The first floor is the first floor. When you enter a building, there's a floor you encounter first. That's the first floor, obviously. You can't enter a building and then leave the floor you're on to reach the first floor unless the place you entered isn't considered a floor at all.
Most of the time I don't care what conventions people use. No system of measurements is right or wrong, it's all a matter of what you're raised with. But this is one of those cases where the convention used by a lot of people is simply wrong and I won't accept it.