We didn't back him "ever so fiercely" against Iran. We sold him some unarmed helicopters and gave him some satellite photos of Iranian military bases.
The rest of his goodies, his warplanes, his tanks, his guns, his sarin gas shells, were French and Soviet/Russian for the most part. And Chinese and North Korean, etc, thanks to Milosovic. Those aren't typical US products we've been digging up in Iraq's deserts or US missile parts turning up in European scrapyards.
In fact, IRAN had more of our stuff than Iraq ever did.
Fact is, it wasn't Iraqi speedboats trying to attack us, or Iraqi missiles being fired our way and Kuwait's way, they was Iranian ones. Shooting up the Iranian navy wasn't for Hussein's benefit, it was for ours.
Well, Ronald Reagan said it differently, though you may know more than President Reagan did.
Reagan armed and backed the Butcher of Baghdad because he was more interested in Iran's partners (at the time), the USSR. Reagan was virulently anti-Communism and he used to remark on it. He dealt with ONE devil (Butcher of Baghdad) to get at another devil, via Iran, the USSR.
Besides, he was mega-ticked off at the Iranians for kidnapping and holding those 44 Americans hostigage for a year.
But, like I said, maybe your knowledge is greater than President Reagan's.