"men don’t have to shoulder the burden of proving that they aren’t misogynists"
I don't accept that. Unfortunately, generalisations such as this are common and all are flawed. What they do is contribute to misconceptions and group mentality rather than individual thought and rationality.
Such a statement is as false as one that claims: "feminists have to shoulder the burden of proving that they aren't misandthrists"
In each case, some will be, some may be, and some will not be.
I accept and appreciate that your piece gave more context and I prefer to think that you do not characterise all men in the same way and that the clause to which I referred was one that escaped appropriate proof-reading.