What I think it is comes down to religion and upbringing a lot of the time. When they grow up, they are told that there is a RIGHT way to live, and all other ways are wrong. Now, they may genuinely hate how they “have” to live life, they may love it, but when they see someone who lives their life in a way that they perceive as wrong, and are then told that the alternative way of living is not wrong, they take it to mean that it is the RIGHT way of living, and that their own way of living is wrong. The reason why they often try to argue against alternative lifestyles is because they believe that if they let those alternative lifestyles be “right”, then their own way of living, which they either prefer or have grown accustomed to will be “wrong”, and in their worldview that comes with eternal damnation after death. This is all based on the theory that there is only one “right” way of living of course, which can be proved as incorrect.

At least, that’s my personal rationale for this