Buddhism and the denial of self
I think the most problematic aspect of the Buddhist worldview is their view of the self. Buddhists believe everything is in a constant state of change. We are like flames. There is no essential self that maintains identity through change. I am literally not the same person I was a few minutes ago. A new person emerges every moment, and the old person goes out of existence. The only continuity between the new person and the old is causal. There is no enduring self, but there is a causal connection between the old and the new.
The first problem with the Buddhist denial of the self is that our knowledge of the self is incorrigible. We can know for an undeniable fact that we have a self, simply because we experience first person subjectivity. If there is consciousness, then there is somebody who possesses it. If there are thoughts and feelings, then there is somebody who is thinking and feeling them.
The second problem with denying the self is that it makes the ideas of karma and reincarnation incoherent. If there is no enduring self, then how can one person be reincarnated? The person who is reborn is not the same person who died. Since there's no enduring self, there's no way to maintain any continuity between the person who died and the person who was reborn. They are completely different persons, so reincarnation isn't even possible. And karma makes no sense either. Why should one person inherit the karma of another person?
Denying an enduring self is extremely counter-intuitive. It makes no sense of accountability. Since I'm literally not the same person who existed a few minutes ago, then I cannot be accountable for what the person did a few minutes ago. If we really took this view seriously, it would make no sense to punish criminals. Why punish one person for what another person did at an earlier time just because this person is causally connected to the previous person?
Denying the self is also counter-intuitive, because it means the memories you have are not your own. You were just caused to have these memories by some previous person who has now gone out of existence. You've got memories of a past you never really experienced since you just now came into existence. And you're about to pass these memories on to some other person who is about to come into existence while you go out of existence. You may remember having something to eat yesterday, but that never actually happened to you. It's not your memory.