Most self-professing skeptics are merely biased against a particular point of view and don't truly believe in their ideology.
They have a tendency to pre-dismiss anything that they perceive as contrary to their point of view. Sometimes they reject every statement coming from an alternate school without listening to its argument. This may be, in part, due to the conditioning by association of falseness with a certain school, altogether. I call it Pavlovian pseudo-skepticism. An example would be a left-winger rejecting, without applying thought, a claim from a right-winger of antiquity of an archaeological site.
On other times, they may reject every statement that appears to contradict what they know already. This is due to an extreme case of narcissism without realising that their knowledge is bounded. One such instance was a recent refusal by my friend (who happens to be well-read) to accept that infinite sets can have different cardinalities. Even after I cited cantor's diagonal argument, he didn't agree, thinking either that I'm appealing to authority without comprehension or that he has limited the scope of Cantor's implication. It is alright not to have known or read about Cantor's argument or aleph number, but rejecting it right away was irritating.
I'm no exception to the above and more fallacies. But, I'm trying to correct myself after experiencing such instances.
Update: As the friend cited in the post has no way to defend his case, this post shall be deemed a one-sided account. However, the issues mentioned in the post are independent of any specific examples.