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So why do these two nations hate each so much?

Because Persia (Iran) is the country of last war before Abramistic Apocalypse according to the scriptures (penultimate was the Syria).
Muslim world knows very well about what Jews asks JHVH under the Wailing Wall (arabic Buraq Wall):
#^https://www.thedailybeast.com/a-christian-group-is-building-a-movement-that-could-destabilize-jerusalems-most-explosive-holy-site
#^https://www.haaretz.com/chasing-the-dream-of-a-third-temple-1.5176045
#^http://christinprophecy.org/articles/the-third-temple/
Muslim world knows very well who pays for it:
#^https://ifamericansknew.org/
#^https://www.alternet.org/2018/05/ex-evangelist-slams-moron-christians-believing-trumps-jerusalem-embassy-will-hasten-jesus-second/
#^https://www.indy100.com/article/president-donald-trump-jerusalem-israel-capital-tel-aviv-evangelicals-apocalypse-third-temple-theory-8096596

Next year, they will probably try to do so as a result of the extension of the Kyoto Protocol. They need a prescribed war in Iran to deprive Palestinians of support for Hezbollah.

Lively conversation here. Let me intervene.

Some religious people claim that there are prophecies in the abrahamic writings according to which a series of wars in the Middle East must pass before the Second coming out (and subsequent Apocalypse). Religious people allege that all last wars in the Middle East after the collapse of the Soviet Union were predicted there. Allegedly, the penultimate will fall Damascus, and the last will be Iran (Persia).

I tried to check this information: i could not find a clear bible prophecy with the schedule of wars, but i find the following references to the destruction of mid-east cities and regions in the run-up to the construction of the Third temple:
- Visions of Daniel 7 about Medo-Persian Empire, revered by most christians, muslims and jews.
- Visions of Isaiah 17 about destruction of Damask (Syria), revered by most christians, muslims and jews.

I am a deeply religious (but non abrahamic), i understand the importance of religion for some people. A sincerely religious person does not know his personal interests; he follows his own religious interest mainly. This is not youth street riots: finding out who is right and who is left. Religious identity has a greater impact on the human body than political/national/tribe identity. Plans of political/national/tribe parties/communities are built for just 4-5 years, less often for decades. Plans of religious communities could exist for centuries, passed from generation to generation.

Concluding my tongue-tied monologue, i would like to cite mentioned biblical prophet ‏יְשַׁעְיָהוּ‏‎:

Who hath heard such a thing? who hath seen such things? Shall the earth be made to bring forth in one day? or shall a nation be born at once? for as soon as Zion travailed, she brought forth her children.

(Isaiah 66:8 King James Version (KJV))