Speaking as someone who comes from a right-wing family, the reason is actually pretty sad and part of the reason I find capitalism so disgusting on a fundamental level (aside from all the obvious stuff).
Their mindset is this: "People are shitty and selfish. The world is eat or be eaten. Survival of the fittest means the big dominates small. Leftism is naive and unrealistic because people are just selfish by nature. I've seen when [insert neoliberal party that people think is left] is in power and they're just as corrupt and dishonest as my boss. Everyone just has to look after themselves and survive the day or they'll go crazy. The best I can hope for is to save myself by getting a lucky break somehow. Maybe if I just invest in the right thing I'll make it big."
Basically, they have been fucked over enough by the system that they no longer believe in empathy or kindness. They see the current system as inevitable and natural because school teaches us that's the the way it's always been. They think that everyone, every. Single. Person. Is only "kind" to get ahead. Everything is cynical and transactional and that's just how we are as a species naturally.
This is why I hate the way we teach ecology. It is still taught in a way that promotes misleading and incorrect interpretation of the natural world and how animals survive and interact. Eugenics may not be explicitly taught any more but it's ideals are still carried forward in the social consciousness by the outdated and irresponsible way life, biology, history and social sciences are taught. That idea of natural order, of survival of the fittest meaning domination of the "weak" without any thoughts behind how social species succeed will be the death of us.
It's been absolutely heart wrenching watching my generation (millennials) have their souls slowly crushed to dust and their hearts hardened by this inhuman system. Millennial middle class liberals and rich chuds might be cringe, but millennial working class right-wingers are truly a tragedy.