Is multi-variable calculus actually hard?

All the time I hear people say that multi-variable calculus is hard. I just don't get it, it's very intuitive and easy. What's so hard about it? You just have to internalize that the variable you are currently integrating/derivating to is a constant. Said differently, if you have z(x, y) and you move in direction x, does the y change? No, because you didn't move in that direction. Am I missing something?