Let's break this down because I am a little confused as to why you and the other poster brought up the inverse of the original argument.
Original Claim: Because I pay taxes I should have a say in how that money is used.
Restatement: If I pay taxes, then I should have a say in how that money is used.
If P then M.
You suggested that the OP is making a mistake because he is rejecting the inverse of his statement and that somehow his original claim is weakened as a result.
You say that OP is wrong to reject "If Not P, then Not M", however the inverse of a conditional statement is NOT logically equivalent to the original statement and as such it's rejection has nothing to do with the validity of the original claim.
The inverse of a conditional does not follow from the original conditional. What follows from the original conditional statement "If I pay taxes, then I should have a say in how that money is used" is the contrapositive: "If I do not have a say in how the [tax] money is used, then I do not pay taxes". That is all, nothing more. You cannot infer anything beyond that from a simple conditional.
I suspect you have committed the inverse error. https://en.wikipedia.org/wiki/Denying_the_antecedent