Sir! Your logic is flawed. Even though you cannot see it. Your logic is flawed.
The flaw in your logic, is that you cannot conceive of there being a flaw in your logic. Therefore, your logic makes no allowance for the possibility of there being a flaw, and in doing so, creates the flaw. Not only can you not conceive of it, and therefore not see it. Your total confidence in your system of logic means that when the spectre of the flaw is raised, you immediately attempt to apply your logic to disprove it's existance. And naturally, you succeed.
The only way for you to fix the flaw in your logic, is to discard it; and then use other peoples logic to analyse your own.
Only once you have applied sufficient other systems of logic to your own system, with earnest and true endevour, and succeded in re-creating your system using their's, will you be in a position to counter their objections to your system, in their own terms.
Only then will you have the ammunition with which to prove the verasity and accuracy of your system, in a way such that they can accept it.
When you have done this enough times that others begin to support your system with theirs, and adapt their's to your's, then you will have cured the flaw in your logic.
You see, no matter that you couch your system in terms that are both familar and classical. If your interpretation of those terms, and your application of them, does not conform to the classical applications, then your system is indecipherable to others, and so, flawed.
Of course, in the process of analysing and accessing your system using other systems, you may discover other flaws in your own, or more benefits in those other systems.
In short, you may decide that your system of logic is flawed. Which it is.