This is like if Hezbollah bombed Yoav Gallant in Tel Aviv. And then Hezbollah starts bombing israeli airports “pre-emptively” because “an israeli attack” (retaliation) is coming.

Yes, exactly. They had good reasons to assume the other side is angry and might do something violent, because they themselves just did something very violent to them! So to protect themselves, they deprive their opponents of means of retaliation. Pre-empting the retaliation.

Hitting someone and then hitting them again because you expect them to hit back does not seem very " self defensy" or “pre-emptive” te me.

I get you. I would totally agree if this was about a school dispute. However in war, there are a number of things which can be done in self defense or to pre-empt an enemy attack which might seem counterintuitive at first, like for example destroying your own infrastructure, or investing in weapons with the intent to never use them.

In war, an attacker can very well attack again to defend themselves and/or to pre-empt the enemy reaction.

If you could hire one of two generals to protect your country; one which considers pre-emptive follow-up attacks and one who would rather let the other side strike back because it seems fair, who would you hire?