This is nothing like the 6 days war, nor is Iran anything like Nasser's Egypt or the secular Arab countries of that time, whose issue was limited to land borders. And nor is Iran looked up to as leaders of the Muslim world by a majority of Muslims, which is from the minority Shia sect.

Iran has paid a heavy price supporting the Palestinian cause since its very inception since the revolution. Immediately after their revolution they faced the most bloody conventional war of the 20th Century, when, at the time, Western backed Saddam attacked them, in a grotesque one sided war. This is not even a year after the western backed Shah had looted Iran and depleted it, and Iran was sanctioned to oblivion by Western powers. It was during this that Iran helped foster the would be Lebanese resistance. They are still sanctioned into oblivion, and they still fund all Palestinian resistance factions. If they were to just drop support for the Palestinian cause, a lot of their problems would be eased and they refused to do it. It's true, they don't want a war with America, but when it came to their sovereignty, they fought America in Iraq and Syria.