Good point, Siebe.
The confusion arises because of the wrong translation of taṇhā as “craving.”
In SN 56.11, the Pali verse is: “Idaṃ kho pana, bhikkhave, dukkhasamudayaṃ ariyasaccaṃ—yāyaṃ taṇhā ponobbhavikā nandirāgasahagatā tatratatrābhinandinī, seyyathidaṃ
—kāma taṇhā, bhava taṇhā, vibhava taṇhā.
As you point out, the translation you quote is “Now this, bhikkhus, is the noble truth of the origin of suffering:
it is this craving which leads to renewed existence, accompanied by delight and lust, seeking delight here and there; that is, craving for sensual pleasures, craving for existence, craving for extermination. SN56.11″
As I have pointed out in recent posts, taṇhā is “getting attached” to something. One could get attached via anger too. One gets attached via greed (craving) or anger because of the ignorance of the Noble Truths. The first stage of understanding those truths is to get rid of sakkāya ditthi.
P.S. Yes. I am glad to see that Johnny has the right idea. I will write more about it in the next post.