Credit note

In GST for the supplier who is liable to issue vredit/debit note ( Refer Section 34 of CGST Act) , there is reason to it.
When supplier issue the CNT/DNT & upload his GSTR 1 , then only the effect of same is get reflected in GSTR 2A of Recepeint.
So yes you are required to issue Credit Note .
Supposing on the basis of Debit from your supplier you reduce your tax liability in GSTR 3B , but what about GSTR 1 .......

So it is mandatory that both should issue debit&credit notes right?

For accounting purpose from both & for GST purpose supplier must issue