a. They have armed and financed their terrorist proxies (Hamas, Hezbollah, Houthis, and others), who used those arms and capital to commit acts of terrorism against their regime enemies (the US and Israel).
b. Witkoff literally offered them free nuclear fuel forever for civilian purposes and they turned him down, bragging that they had enough highly enriched nuclear fuel already for nuclear weapons
c. I can put 2 and 2 together
In what universe does having nuclear weapons protect you from getting schools and hospitals bombed? Israel very likely has nuclear weapons, but Israeli schools and hospitals are getting bombed by Iranian missiles. So what?
Can we believe anything that the senior people in the current US administration say, at this point in time?
With all this considered I think it is clear why Iran is able to bomb Israel back and Israel can't just nuke them.
I think the points you made about why Iran would give nuclear weapons to terrorists make no sense. Because Iran would, presumably, get obliterated when those terrorists use those weapons on any country.
As far as I know, full-on invasion of a country that has nuclear weapons has never occured in history so far. So Iran having nuclear weapons in a defensive capacity is obviously good for them. In fact all countries having nuclear weapons in middle east might have made it more peaceful but would have been obviously terrible for Israel/USA