Andrew Gelman wrote a parody of arguments against Bayesianism here. Note that he says that you don't have to choose Bayesianism or frequentism; you can mix and match.

I'd be obliged if someone would explain this paragraph, from his response to his parody:

• “Why should I believe your subjective prior? If I really believed it, then I could just feed you some data and ask you for your subjective posterior. That would save me a lot of effort!”: I agree that this criticism reveals a serious incoherence with the subjective Bayesian framework as well with in the classical utility theory of von Neumann and Morgenstern (1947), which simultaneously demands that an agent can rank all outcomes a priori and expects that he or she will make utility calculations to solve new problems. The resolution of this criticism is that Bayesian inference (and also utility theory) are ideals or aspirations as much as they are descriptions. If there is serious disagreement between your subjective beliefs and your calculated posterior, then this should send you back to re-evaluate your model.