Questions about strong acceptance of rebirth? In a nutshell, the Buddha's teaching is:


self-views ("I have a self" and/or "I have no self") must be avoided
craving is a precondition for suffering, thus we must train ourselves to gain control over craving and, finally, to eradicate it
nihilism ("non existence") and/or existentialism ("existence") must be avoided
being spiritual or having spiritual views is better than being materialistic or having materialistic views
extremes must be avoided (middle way)


I'm wondering WHY a strong belief in rebirth does not conform with the above Buddha's teachings? I really want to understand the WHY behind it. WHY a belief in rebirth does not lead to the cessation of suffering? WHY somebody who strongly accepts rebirth (read the below case to see what I mean by "strongly accepting rebirth") can't attain Nibanna?

Please respond to the below questions that I provided and then if you wish give your explanations/answers.



CASE a)

Suppose person X STRONGLY ACCEPTS REBIRTH by claiming: "There's NO WAY that after death there is no life. Life after death doesn't stop. Life after death is real. Life after death can't stop." When asked "Can life after death come to an end for an arahat?" person X would answer: "No. There's NO WAY life after death can come to an end. Life after death does not come to an end for all beings, even if a being is an arahat or attained enlightenment (Nirvana).". When asked "Is there at least any tinyyyy possibility life after death can come to an end for an arahat?" person X would answer: "No. There's NO WAY! I know there's no way! NO WAY.".

Suppose person X is very sturdy and close minded and there's no way person X will change his/her views about life after death, not even if somebody would threaten his/her life and would actually kill him/her.

Questions:

1a. Is strong acceptance of rebirth in the above scenario, a result of craving? Why?

2a. Is strong acceptance of rebirth in the above scenario, a result of nihilistic ("non existence") and/or eternalists ("existence") views? Why?

3a. Is strong acceptance of rebirth in the above scenario, a result of a view regarding self ("I have a self" and/or "I have no self")? Why?

4a. Can an arahat strongly accept rebirth, just like person X in the example above? Why?
The question is basically, why is belief in literal rebirth (reincarnation) a problem. I won't address every OP point here, just make four theses:


Rebirth is self. Self is rebirth. Whenever there is belief in rebirth, there is attachment to self. You can't possibly believe in rebirth without having a notion of entity (identity) that is getting reborn. Having a notion of entity means you don't understand sankharas (assembly of phenomena), which means even your understanding of anicca is superficial, let alone of anatta or shunyata.
Rebirth usually (but not always, see next point) involves dualistic views about some "special" substance that carries on the entity's identity. That substance is imagined to be made from something principally different, a second kind of stuff (first being normal matter/energy) - hence "dual-ism". Whatever you call that stuff, it basically means "soul" - some spiritual supernatural essence.
Even if you define rebirth as arising of the new being on the basis of the previous being's karma (like the old candle transferring its flame to the new candle) - in other words if you define rebirth as transfer of information/causation - if you imagine this process going 1:1 from one previous being to one new being through some mysterious mechanism, you are still creating a cohesive entity where there is just a bunch of disjointed causation chains. The information/causation is transferred all the time, many-to-many, not at the moment of death or birth. So transmigration of sentient beings at large is real, the wheel is continuously in motion rolling in the rut from generation to generation. Karma is real. But individual reincarnation is not. 
If you look deep inside you will see that rebirth is a byproduct of a psychological need. What need? A need to have something beyond THIS to look forward to, to hope for, because THIS is unbearable. But denying THIS is denying the first noble truth, it is escapism. No progress on the path can be made until we accept THIS with all its pain. We must fully come to THIS because THIS is where Enlightenment unfolds.


My recommendation is to meditate on the notion of entity. Think about a piece of wood and how it becomes ashes as it burns. Where are the spatial/temporal boundaries of an entity here? Same with ice/water/vapor. Same with an entity called "a river". Same with people, including both body and mind. Where does the mind come from? Where are its boundaries? Is there an entity here?