[Lafclaria]

The Cha Chaka Sutta (M148) tells us:

"Dependent on mind and mind objects [could be the "poem case" as mind object], mind-consciousness arises. When the three meet, there is contact. Dependent on contact, there is feeling, dependent on feeling there is craving.

[...]

If one were to say, craving is self, this is not fitting. For the arising and passing away of craving is seen [discerned].

Where is re-birth from this "passing away" if it has passed away?

I'm not sure I understand you. I'm not saying craving or anything else is self, and I'm not saying self is reborn. I don't see a self to be reborn. I don't think people are reborn because I don't think that people are selves or entities at all. There is the arising and cessation of phenomena, but phenomena aren't, by definition, entities. Phenomena can be reborn when they are picked up on and repeated, or even just aspects of them. Maybe that's the source of our confusion?

In other words, to say that there is rebirth is not equal to saying that there are people or selves that are reborn.

As is commonly known, suttas can seem to contradict each other here and there because the Buddha adapted his words to the audience. If the suttas where the Buddha talks about rebirth of persons, then maybe his immediate audience was incapable of understanding a more advanced teaching. Anatta and rebirth are not contradictory, because phenomena are reborn, not selves.

Sorry if I'm not explaining my ideas clearly enough!