Deeply ingrained religious pride. JWs have been indoctrinated with the head-swelling idea that they alone have the true religion and everyone else is in error and serving satan. They also tend to point scornfully and ridiculingly at all other religions, because of the errors they teach.
So in the JW mind, teaching truth is associated with being the true religion and accusing a religion of teaching falsehood is associated with labeling the religion as false and ridiculing it. They have been conditioned to think this way. So when you point out errors in Watchtower teachings to a JW, in his mind you're treating his religion with the same disdain that they treat other religions - you're accusing his religion of being false and you're ridiculing it.
Another important reason is that JWs are extremely patriotic - idolatrously patriotic - toward their organization. They have been indoctrinated to esteem the JW organization and it's governing body as being as essential to their salvation as faith in the bible and Jesus. To the JW faith in the organization is as important as faith in God. So they equate any criticism of the organization with blasphemy against God and see it as a threat to their spirituality.
To use a sports analogy: JWs are like fanatic supporters of a soccer team(Watchtower organization), who love and idolize the team more than the game itself(worship of God). Tell them you're not a soccer fan and they might be a little disappointed and try to convince you that it's really a great game. But tell them their team isn't all that good and get a good beating.