I can't really add much about what exactly makes hoax-believers tick, but over the years have noticed four particular qualities in most of the vocal ones who put up a fairly good fight:
Young
Smart
Undereducated
Arrogant
Naturally there are variations and exceptions – we've had some who are old, smart, undereducated and arrogant. Some HBs obviously have an above-average IQ, but not the education to back it up so it works properly, such as the having ability to think and debate logically. More often than not, their under-education applies to Apollo – they don't know much about it, don't understand it, and so they rubbish it. Some of them might be quite smart, but they have much more ego than brains – a very poor combination.
Fifty years ago I had all of the first three qualities and, thankfully, not much of the fourth, but I sometimes decided some procedure needed changing and bumbled in before I fully understood exactly why things had been done a particular way for a long time. Got into trouble a few times before I understood the understanding part.
I left school aged 15 in 1964 and went to work in a world that was heavily populated by old, vocal Victorians (the era or state of mind, not the State in Australia) and to whom modern-day PC-Brigaders are very similar. I didn't know how to best handle them.
Looking back now, I can see that school was too boring, not practical enough and not interesting enough. A lot of useless facts were rammed into my head and I was supposed to regurgitate them, but I certainly didn't get an education for living, and my parents hadn't helped either. There was nothing about relationships of all kinds, professional and personal, nothing about how and why things were done in the business world, and more importantly, nothing about logical thinking which I only learnt here and at the Bad Astronomy Bulletin Board in the 1990s, thanks to JayUtah and others. And the biggest thought I have about that is, “Why the hell wasn't I taught that valuable stuff at school, before I was old enough to leave?” I firmly think the world might be a better place if many more people were taught basic practical and logical thinking at an early age.
Because of the above, I often see my if-I-had-run-off-the-rails young self in some HBs, and feel sorry for them.