In an argument, generally both parties are making claims. One is making a a claim of X, and the other is saying or implying that X is wrong (such as in this argument).

Both of these things are claims, and therefore both parties should have the burden of supporting their positions. The idea of 'onus of proof', at least as it's normally used, is poisonous as it's just used as excuse for one side of the argument to dismiss the other's with apparent impunity despite the fact that each person in the argumentis attempting to put forth a position.

(Some people say the one making the 'positive' claim is the one who automatically has the burden, but that's meaningless; sometimes the positive claim is the more outlandish and sometimes the negative one is; a positive claim can often be reworded to be a negative claim and vice versa; and often, such as in our discussion, there isn't even a positive verses a negative claim anyway. And, of course, even when the positive claim is the more extraordinary of the two, if a Person B claims it's false then he/she should his own burden of proof as well; otherwise we're giving bias toward nothing true ever being extraordinary.)

Just to be clear, this response deals with the dismissal of my claim regarding how one should think or what 'true critical reasoning' is, not claims in general of the type that would dismissed according to Hitchen's Razor; though some of what I'm saying applies to the latter too.