Well, things cannot be "inherently incorrect" for no reason - the question is why and where exactly is the proof incorrect.

Finding the mistake is a nice little exercise for un-dulling the brain, which provides a small "aha!" discovery moment. Such small discoveries are in fact among the nicest things in math and "real science" in general. Here you get a chance to experience them first hand, without the need to be a real mathematician or a scientist.

Don't ask your "math friends", you'll ruin the point. Try finding the bug yourself - in this particular case it is not too hard - just substitute some arbitrary suitable numbers for a, b, c, step through the proof checking whether each equation holds with these, and you'll see what is happening there.