Every time I've tried to understand the entire argument it just raises more questions to me. For example as I was first introduced to it, frequentists simple count frequencies observed in nature and then compute stats on them, and then build inferential models using those stats without assuming any complex underlying distribution. While Bayesians count frequencies, apply a prior correction (say, adding a pseudocount of one for every unobserved possible event, or any other way of assuming the generative process has a distribution that we've previously estimated), some stats,then build models from that.
however, after I was told that, I've seen several other arguments that quickly dive into: the distribution of the underlying events (I've heard that frequentists assume one type while bayesian assume another). Other folks just sort of give the example of the base rate fallacy.
Throughout all of this I've realized: I don't understand stats at all. I came to the scientific world with a view much more like physics: there is a microscopic event system (a particle simulation, or whatever) that we are observing, but due to limitations, we can only make macroscopic observations, which represent biased aggregations of the underlying microscopic event system. We can figure out those biases and use the aggregate data to build predictive models of the underlying systems- without ever really knowing the true details of the microscopic model.
From what I can tell, everything about what physicists do to model the world mentally is more Bayesian than Frequentist, if I understand what the hell people mean when they argue about it. However, as I said, every time I look at the arguments, I realize I don't understand stats, while I understand the physics approach which seems to be fairly obvious.