I'm going from memory, but I seem to recall that according to the book "The Israel lobby and US foreign policy", Irsael was initially lobbying against US invading Iraq because Israel wanted the US to invade Iran and thought Iraq was a distraction. Then, someone in the US convinced Israel that Iraq was going to be really easy and the US would do Iran right after, and Israel stopped being against invading Iraq. And this version is way funnier than yours.
https://transcripts.cnn.com/show/se/date/2002-09-12/segment/...
The reasoning? "Saddam cannot be allowed to have nuclear weapons"
It's crazy how little people seem to remember that we completely made up this insistence that Iraq had nuclear weapons (which is THE "WMD" we were screaming about before invading, not the chemical weapons!) which there was never any evidence for.
We fabricated cassus belli like the real world is some sort of Crusader Kings DLC, including the stupidly transparent nature of the fabrication.
https://en.wikipedia.org/wiki/Niger_uranium_forgeries
https://en.wikipedia.org/wiki/Iraqi_aluminum_tubes
Like, so many people seem to have just straight up refused to remember that we did this all before! The most innocent reading of our Iraq invasion is that Bush himself was so stupidly convinced of Saddam's evil that he refused to accept direct evidence to the contrary, and even that is an enormous red flag.
And yet, stupid americans still voted for him again. God forbid there be consequences for Republican Presidents lying directly to the public to put us into an unfunded war for years that we did not need and can't afford the debt for.