Furthermore, don't think of the two as being exclusive! They're not separate. Discreet mathematics is a _subset_ of real analysis. When you jump right into discreet mathematics, you're just skipping lower-level details of analysis.
Being about "how not to use math" and about math as such are pretty different things. It's like you were teaching a class on car repair and assigning a book on consumer fraud.
No. It's like you were teaching a class on car repair and telling your students how to not screw up. e.g. "Do not ever adjust the stabilizer based on popular arguments such as ___ and ___ because it will only screw with the engine and may even cause permanent damage." It's actually very relevant, especially in the early stages of learning.