The other major problem with denying/questioning/not believing in rebirth is karma. How does one explain the variety of life circumstances experienced by (or into which are born) individual beings? Pure luck? What about beings that do not (or cannot, in the case of animals, to limit our discussion to beings with physical form) come into contact with Dharma? Condemned to suffering with no chance of ultimate liberation? What about dependent origination? How does one explain that without recourse to previous lives and karma.
None of those things actually requires an "explanation", except that not having an explanation for the 'why' of things tends to be unsettling for many people...but this is just a sign of clinging to a self.
"Pure luck" is as good an explanation as anything else. "Pure Luck" may not seem as plausible
to you as karma, but karma does not seem as plausible
to some people. There are plenty of causal reasons for why things appear as they do, for instance, why planets tend to be round. So one event does lead to another. It's not as if things just take whatever appearance for no reason.
As far as beings who do not come into contact with the dharma, beings do or do not, because of many factors. Saying it's because
of a being's karma may be true, but it is really a moot point. It's like saying that it was my shadow's karma to appear when the sun came out. It makes "karma' into a kind of manipulating force on its own, like gravity. Yes, it is a being's karma, meaning the result of previous actions that brings one or does not bring one into contact wit the Dharma. But "karma" is not a cosmic manipulator or balancing scale of events.
I think that this is a view of karma that many who reject the idea of karma reject. But they are really rejecting a misunderstanding of karma, one that they take for a proper understanding. Same with rebirth.
Likewise, dependent origination, the assertion that all things arise and exist (appear) in complete relation to other things is a perfectly valid materialist viewpoint. One can hold that view without believing in rebirth.
One can hold the view that karma only refers to the causes and results associated with one's actions of body speech and mind in a single lifetime, and that a single lifetime is all that one gets. This is not my view, but it is an understandable view, because this lifetime is the only one a person directly experiences.
These are not the points where the rejecting of rebirth fails. In fact, one could argue, from a traditional buddhist viewpoint, that ultimately no rebirth occurs, that these realms are merely a projection of the mind.
And this, I think is the root of the division: Does the material body produce the experience
of the mind, or does the mind produce the experience
of the physical body? To the person who asserts that the experience
of the mind only occurs in this lifetime, it must be likewise asserted that the experience
of mind is produced by the activities of the physical body (the brain, central nervous system, etc.) but this, to me, is no different than saying rocks and trees have spirits (a notion that most materialists would reject).
It can be shown that when your finger touches fire, an electrical signal goes to the brain and a burning sensation is felt in your finger. This is all fine and well. It is not different from turning on an electric lamp. But who
is experiencing this electrical charge, who
interprets it as pain? This is the question that the materialist view does not answer. This is where the rejection of karma and rebirth starts to fail.