I've spent many years studying YEC and interacting with YEC's. I've even spent some time on the YouTube YEC debate circuit. I've come to one over-arching conclusion: the roots of YEC belief go down to the very foundations of one's philosophical outlook. Specifically, it is rooted in an acceptance of teleology [1]. It is a very long chain of reasoning from there, but this it the thing that most detractors of YEC miss: this reasoning is logically sound [2]. And because of that, you cannot successfully combat it with logic. You have to go to the very roots of the belief and address its foundations, which is to say, you have to deal with the fact that YEC's accept teleology as a philosophical foundation, and it is very hard to dislodge someone from that position without also sending them into a spiral of existential despair. That is the reason that these beliefs are so persistent despite being so violently at odds with [EDIT: the scientific view of] reality.

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[1] Teleology is the assumption that things have a purpose. The divergence between teleologists and whatever its opposite is (scientists?) is that the latter starts by asking what is the cause? and the former starts by asking what is the point? Everything can be traced back to that initial flapping of the butterfly's wings.

[2] An extremely abridged version goes something like this: a cursory inspection of the world around us seems to indicate that it was designed. So let us adopt that as a hypothesis. What would be expect to see? Well, one thing we would expect is that the designer might have provided a manual to go along with his/her/its designed creation. And lo and behold, there is such a manual. Actually, there are many such manuals. Collectively they are referred to as holy texts. The logical rabbit warren branches out from there.