One which seems easy to jump to immediately is that they are lying. They know that their argument is flawed and they don't care, they think repeating it as if there are no flaws will be effective for the general population. I definitely think this is true of (most of) the professional apologists. They know the arguments extremely well and they generally seem to be intelligent. Certainly they can see the enormous glaring holes in them. They are either true believers who are only interested in converting people (or keeping their flock), or they are profit motivated. Either way, fuck those guys.
But a third possibility is what has really interested me and has been rolling around in my brain going for the last few days. These are people who are bouncing back and forth between what they can see through logical argument and the indoctrination that is embedded deep within their minds. I find this the most interesting because I was in this state for a number of years. To be fair, it was mostly internal argument that I was having with myself on long car trips, but I'm pretty sure it would have been similar if I had a regular debate partner.
Even when I thought I had a perfect argument against Christianity on one day, I was able to convince myself on another day that there was a flaw in my previous argument. Now, imagine if I had been arguing with atheists rather than with myself. How would this have played out? The atheist would have produced an argument against me, and perhaps even convinced me that they were right. I would have thought about it the next day and convinced myself that the atheist had been incorrect, then I would have gone back to my original argument as if my conversation with that atheist had never happened. I wouldn't be lying, and I understood the atheist's argument (at least at the time), but nevertheless I would have been back to square one. Indoctrination is a bitch!
So I ask myself, how did I break out of this? It's all about repetition. Each time I had to do the mental gymnastics it was a little bit harder. There's a new wrinkle to the argument, a new aspect I had to get around. I was able to do it for a long time, but eventually the house of cards came falling down. I've always been a detail oriented person, so I was only able to push my concerns to the side temporarily. Eventually they would push themselves to the forefront of my mind and I would have to admit to myself that my patchwork to explain them away wasn't quite adequate. I did this mostly on my own, but I think a lot of people could use a push to keep considering their arguments. They aren't going to reevaluate their patchwork themselves, they need someone else to keep poking at it. Every time they present their poor argument, someone needs to point out the flaws. It's that repetition that is necessary to get through the indoctrination.