Now you have weakened the generalization to the point it's meaningless.
What act exactly do people believe to be in their self-interest? Why are you claiming it's the anti-social ones and not the pro-social if the believe is not rooted on reality?
If you want an example, I guess the enthymeme would be:
a) Internet privacy is in one's self-interest
b) Many erroneously believe privacy on the internet to be goal of terrorists, hackers, etc.
c) A subset of these people then act against their own self-interest by vocally supporting mass surveillance, or voting in candidates who do so, in the name of the apparent self-interest of safety
I also didn't say anything about pro/antisocial people... different person.
Belief is categorically not rooted in reality. That's why it's called belief and not fact.
Humans are intrinsically irrational. That is a plain and simple fact. Humans operate exclusively on what they think is true instead of what is objective fact. Subjectively an individual human acts in ways that are roughly rational and coherent within their belief system and world view. The problem is that this frame of reference is entirely subjective and is only tangentially related to consensus objective reality. Assuming that you can apply your own reasoning and logic to all other humans is fallacy.
You must accept the fact that other people do not share your world view and will not act with what you, personally deem to be rationality.