I would add only that, sometimes, knowledge of the calculus tricks does aid the understanding. But the math is the servant; it adds precision to stories that can be explained in other ways.
And just because you can take derivatives and integrals doesn't mean you understand economics. If you can't explain opportunity cost, consumer surplus, deadweight loss, elasticity, etc. in plain English--which is what this class is supposedly teaching you--then you're just doing math problems.
If this guy could do that before taking the intro micro class, then he may be right that the class was a waste of his time. But most people can't. In fact, since I was a TA for this class for four semesters, I can tell you that a lot people can't do that even after taking the class. To tell them to skip ahead to micro with calculus is a terrible idea that would hurt, not improve, economic education.
QUOTE OF THE DAY. A Constrained Vision, distinguishing economics from applied mathematics.