The concept of a "burden of proof" is often misapplied. If you believe something, then you have a duty to justify it, no matter what it is. If you think A causes an increase in X, you do have a duty to provide evidence in support. If your friend thinks B causes an increase in X, they have a duty to provide evidence in support. There is a burden of proof on both sides.

The burden of proof is most often used to say that an unusual claim, one that departs from the norm, needs more evidence in support. This is true; an a priori unlikely claim requires more evidence, in the Bayesian sense, to raise its probability close to 1. However, it can only be applied if both participants in the discussion agree on what the norm is. Clearly, the two of you do not, so if either wishes to persuade the other then they have a burden to produce strong evidence in favor of their claim.

We might say that the basic problem is that your friend is not trying to persuade you, he's trying to affirm his own beliefs. From his perspective, "B causes increase in X" is the norm, and any departure from that norm would require a lot of evidence to change his own mind, so that is why he says you have a stronger burden of proof. It makes sense to him and affirms what he already thinks. But it is completely ineffective at persuading you, because you have a different norm, and from the perspective of this other norm, "B causes increase in X" is the departure that requires more evidence.

So, he's probably not trying to persuade you, he's just trying to make himself feel better about his own views. And that's the problem. In a discussion we should try to make arguments that appeal from the other person's perspective, not our own.

See also this SMBC comic.

The concept of a "burden of proof" is often misapplied. If you believe something, then you have a duty to justify it, no matter what it is. If you think A causes an increase in X, you do have a duty to provide evidence in support. If your friend thinks B causes an increase in X, they have a duty to provide evidence in support. There is a burden of proof on both sides.

The burden of proof is most often used to say that an unusual claim, one that departs from the norm, needs more evidence in support. This is true; an a priori unlikely claim requires more evidence, in the Bayesian sense, to raise its probability close to 1. However, it can only be applied if both participants in the discussion agree on what the norm is. Clearly, the two of you do not, so if either wishes to persuade the other then they have a burden to produce strong evidence in favor of their claim.

We might say that the basic problem is that your friend is not trying to persuade you, he's trying to affirm his own beliefs. From his perspective, "B causes increase in X" is the norm, and any departure from that norm would require a lot of evidence to change his own mind, so that is why he says you have a stronger burden of proof. It makes sense to him and affirms what he already thinks. But it is completely ineffective at persuading you, because you have a different norm, and from the perspective of this other norm, "B causes increase in X" is the departure that requires more evidence.

So, he's probably not trying to persuade you, he's just trying to make himself feel better about his own views. And that's the problem. In a discussion we should try to make arguments that appeal from the other person's perspective, not just our own.

See also this SMBC comic.