The first time that I realized this was when debating certain frum Jews about the scientific validity of evolution. It dawned on me that their claim of wanting to debate and discuss the scientific merits of evolution was a sham. They were fundamentally ideologically opposed to it, rating it as heresy. A scientific discussion, on the other hand, means drawing conclusions from the physical evidence without any preconceived notions. So there was no scientific discussion taking place, and any pretense at such a discussion was futile and misleading without the underlying theological dispute being resolved.
I just noticed another example of this in a comment thread over at Hirhurim (which, incidentally, recently featured a fascinating post about the Torah-Science controversy). In a discussion about the ikkarei emunah, a ferocious and lengthy debate - 195 comments! - took place between one Rabbi Shalom Spira and some other people. The topic was whether there have been accepted Torah authorities who acknowledged that Torah scrolls are not word-perfect, and whether there is any evidence of this. Rabbi Spira insisted that there are no such authorities and there is no such evidence, while a number of people insisted that there were and there is.
I don't know why they wasted their time.
His opponents completely missed the point. This is not a matter of whether there is evidence supporting the conclusion that there were great Torah scholars who accepted that Torah scrolls are not word-perfect, and whether there is evidence showing that they are not word-perfect. It is a matter of a religious belief. Rabbi Spira was completely open about this! I quote:
...a Jew is indeed absolutely required to accept Rambam’s eighth principle, viz. that every single word in our Sefer Torah was dictated by HaKadosh Barukh Hu to Mosheh Rabbeinu.
...the Ibn Ezra will not inform us of the Halakhah on this matter, when the gemara has already clarified what the Halakhah is. Instead, it is appropriate to give a forced explanation to the Ibn Ezra in order to judge him favourably that he was an Orthodox Jew.
...Epistemologically speaking, history is a matter of belief – not science (because all evidence we have regarding events that occurred prior to our birth is circumstantial and second-hand in nature), and the Torah governs how we are to appreciate history. When the Ribbono Shel Olam reveals Himself at Mount Sinai with the declaration “Anokhi… asher hotzeitikha me’eretz mitrayim”, it is a declaration that we must interpret history in accordance with the theological norms of Judaism. And one of those norms is to recognize that our Sifrei Torah are word perfect.
To engage in a debate about the evidence is to further enhance the mistaken impression that there is an evidence-based epistemology being used. There isn't. It is a religious debate, not a scientific or historical debate. And that is why they failed to convince him. They were engaged in the wrong argument.