that's because you've been lied to, the Catalyst does react, it just reacts both ways, first one direction then the other, so in the end your Catalyst comes out of the reaction in the same State it went in.

The catalyst is something that reacts with one or more of your reactants, forming a transition state that will then react with your other reactants faster or more efficiently. So Teachers saying the Catalyst doesn't react are just straight lying, that's not even a simpification, it's just wrong and i don't understand the reasoning why you wouldn't just explain that it does react, but comes out of the reaction in the same State that it went in.