B: Prove it!
A: No, you prove first! With really rigorous thinking, please!
People are doing A. Someone says "Do B instead!". "Why should we do B?" "Well, why should you do A?" At the end of that extremely unproductive exchange, what are people going to do, A or B? They're going to keep doing A, because they were already doing that, and nobody gave them any actual reason to change.
So "burden of proof" isn't meant in the sense of this being a formal debate, with rules. It means that, when ahf8Aithaex7Nai said "Prove your own claims before you demand proofs from other people", that ahf8Aithaex7Nai is wrong. OOP is the current default in terms of the bulk of professional programming; if FP advocates want that to change, it's on the FP advocates to provide reasons, not on the OOP advocates to prove the correctness of the status quo.
The proponents of status quo only need to prove that the existing approach works and is useful. And I think that is proven already by the very existence of status quo. It wouldn't be there if it wasn't somehow useful.
I hear this often. In the past the claim used to be that they "think" object-oriented. This is a thinly veiled argumentum ad naturam.
> ... on the functional proponents to prove
Prove your own claims before you demand proofs from other people. And by prove I mean really rigorous thinking, not just superficially seeking confirmation for the things you already believe either way.