I heard that it was wrong and we use:
We'll meet next Monday.
This is apparently because we don't use on before next. Is this true and why? It sounds good to me. Is it just an idiomatic thing?
Is this true?
It sounds good to me
No... it sounds incorrect.
Why? Is it just an idiomatic thing?
Yes, most likely. There are probably thousands of things in English (or other languages also) which are "just idiomatic".