Here’s 3 reasons why.
1. Cognitive dissonance
Just imagine you would have to be open for suggestions that challenge your current belief system. It potentially could mean that you would have to revise this belief system and, ultimately, your comfortable way of life. There’s too much at stake for your average kiruv clown to even start considering the option of the other person being right: It may lead to the disintegration of the family or financial insecurity.
Now, just because I see this question coming: these are same reasons why skeptics like me decide to stick to their current lifestyle (at least, for the moment). However, there is an important difference: at least skeptics are willing to listen to what the other guy has to say. What you do with that information is for you to decide.
But there are more interesting reasons why it doesn’t pay to debate religion with the religious…
2. You stick to the original information
In Why You Think You’re Never Wrong (and What to Do About It), Lifehacker quotes a Scientific American article called Lingering Lies (note: you have to pay for the full article):
Once an idea enters your mind it's hard to get rid of it. Even after you've been proven wrong and know that you are, your brain is wired to stick with the original information. It even influences you subconsciously. This makes it exceptionally difficult to actually feel wrong even when you know you are. Scientific American has the explanation of this phenomenon:
Psychologists asked college students to read an account of an accident involving a busload of elderly passengers. The students were then told that, actually, those on the bus were not elderly. For some students, the information ended there. Others were told the bus had in fact been transporting a college hockey team. And still others were warned about what psychologists call the continued influence of misinformation-that people tend to have a hard time ignoring what they first heard, even if they know it is wrong-and that they should be extra vigilant about getting the story straight.
This is one of the reasons why it is so difficult to shake of the frum belief system.
3. Debating only strengthens beliefs
Now don’t get me wrong here. I am not saying that their arguments are better so we’d better stay out of their way. Quite the opposite.
Once something is added to your collection of beliefs, you protect it from harm. You do it instinctively and unconsciously when confronted with attitude-inconsistent information. Just as confirmation bias shields you when you actively seek information, the backfire effect defends you when the information seeks you, when it blindsides you. Coming or going, you stick to your beliefs instead of questioning them. When someone tries to correct you, tries to dilute your misconceptions, it backfires and strengthens them instead. Over time, the backfire effect helps make you less skeptical of those things which allow you to continue seeing your beliefs and attitudes as true and proper.
It is the same reason why you double-check your weighing scale if the weight seems to high but you never double-check it if it tells you that you lost some weight.
Tachles: If someone is wrong and passionately believes he is right, not only are your chances small you will win the argument, but you may end up strengthening his opinions.