Why are Iran and Israel enemies?

usa and other western governments supported the shah's unpleasant regime

when the revolution kicked him out, the people showed their displeasure at the usa, resulting in a massive hissy fit by the usa and allies which remains to this day, decades of sanctions and other punitive actions

the usa is a bad loser, see cuba, vietnam etc., it's counter productive as it is simply pushes likely neutrals to it's own foes, norks, russia, china, syria etc.

israel backed/backs the usa in this, hence enmity

I think the general consensus is Khomeini's ideological position caused all ties to be severed after 1979. For a variety of reasons, the Islamic regime does not recognise Israel as a legitimate state and the two countries have fought a proxy war ever since.

Having said that, when it is in their common interest, they do work tacitly together Israel supported Iran during the Iran/Iraq war in the 1980's. Israel have pursued what it called "The Periphery Doctrine" for decades which is focussed on creating closer ties with key non-Arabic nations in the Middle East, Iran included.

It is hard to know what the latest Iran attack was really meant to do. They basically telegraphed it and would have known their missiles would be intercepted. You could argue it was posturing on Iran's behalf, or you could argue it was a definite statement of intent to show they were prepared to attack Israel.

As for relations between the two improving, whether covertly or overtly in the coming years, very hard to see how that would happen now.

because even after all this time, the 'west' led by the usa won't stop sanctioning/attacking them

israel is an eager participant in this as it helps bolster american support, as well as providing a convenient example to any other uppity local states

the iranian regime is appalling, but failing to engage or reward 'good' behaviour simply fuels an ever more extreme position, at the cost of whatever more moderate voices remain in iran