What is translated as ‘origin of identity’ is compound Pali word sakkāyasamudayo.
Maybe these annotations can help you understand it in different way (if you understand which i hope you do then thinking in lines that ‘twins provide interesting perspective on identity view’ will cease…) :
sakkaya
the body in being [??], the existing body [?? these definitions are in line with sakkayaditthi i.e. ‘wrong view’…] or group (= -nikāya q.v.); as a t.t. in P. psychology almost equal to individuality; identified with the five khandhas MN.i.299; SN.iii.159; SN.iv.259; AN.ii.34; Thig.170, Thig.239; Dhs-a.348. See also DN.iii.216 (cp. Dial. Pv.iii.216#1); AN.iii.293, AN.iii.401; Mnd.109.
-diṭṭhi theory of soul, heresy of individuality, speculation as to the eternity or otherwise of one’s own individuality MN.i.300 = MN.iii.17 = DhS.1003, SN.iii.16 sq In these passages this is explained as the belief that in one or other of the khandhas there is a permanent entity an attā [like ‘being’ or the ‘existing body’, for example!!]. The same explanation, at greater length, in the Diṭṭhigata Sutta (Pts.i.143–Pts.i.151).
samudaya
rise, origin
I would not translate or explain kāmataṇhā bhavataṇhā vibhavataṇhā as ‘craving for sensual pleasures, craving to continue existence, and craving to end existence’ but 1. - as reacting to and wanting to engage in some kind of sense experience ‘I want to go to beach’ [to look at the sights] or ‘I hate the noise in the city’ 2. as wanting something to be ‘Let there be democracy’, ‘I want to be rich’ 3. as wanting something to cease to be ‘I hate being poor’ ‘I want Trump to be impeached and not be the president anymore’
To crave or even to think of ‘continued existence’ or ‘ending existence’ one must think in lines of the belief that in one or other of the khandhas there is a permanent entity an attā which would be the thing which would go on to continue existing or cease to exist! 
Interesting i just notice that in the sutta it actually starts with explaining it like that (i.e. in relation to ‘five grasping aggregates’) and the thread i posted about selfexisting things in ones experience also was somehow about this same thing but for some reason i dont see that anyone actually understands what is being said there, i.e. body / identity being made in relation to the ‘five aggregates’ is ignored. The objects and ‘identities’, body and bodies are made of/by the five khhanda basically. In simple terms what you think of yourself or some ‘object’ is idea made in relation to a collection of pictures. I think the bulk of the problem comes from thinking of ‘rupa’ as physical form or object or something like that and in similar way to not understanding the rest of the five constituents of the process of perception ( rūpa, vedanā, saññā, saṅkhārā, viññāṇa) for what they really are.
Even the word ‘aggregate’ has connotations in line with sakkayaditthi or ‘personality perspective’ i.e. wrong view. And thinking of rupa as ‘physical form’ ‘object’ or alike also incorporates sakkayaditthi! And if you think of bhavatanha as something in relation to some identity / entity continuing its existence that is also in line with sakkayaditthi! Even the translation of viññāṇa as ‘consciousness’ has connotations of some sort of seer having the ability to be conscious or consciousness being the seer or of some sort of entity being seen. Its everywhere but in the original text! How can one possibly understand?
