No, you are not the problem, at least not wholly the problem, the combined effect of your method of replying and people who have persistent disagreements might be though.
You probably know this pretty well, but statements of fact(or statements in fact form), whether or not they are correct, tend to rub people who are looking for the reasoning the wrong way, especially when your reasoning is broken into multiple, apparently distinct 'facts', such that no possibility of error on your part is assumed to be possible(or hell, possible at all). It may be perfectly good logic, but wouldn't convince anyone who already has a stand.