The fear isn't really that Iran will start a nuclear war with anyone. That doesn't happen, obviously. The fear is that they will point their missiles, and then do what they like, with all the rest of us knowing that if we make much of a stink they'll fire them at Israel.
It's like gambling with a big stack. You can't bluff with a few chips. You go all in and the other guy laughs because he can absorb the damage. The damage they could do to Iran before they were stopped now isn't small, mind you, but it isn't anything that would put a black mark on history.
If you look at international politics, nuclear weapons are just bluff material. If they decide to invade, say, Lebanon later, the US would be vastly more hesitant to get involved. Why? Mainly because Iran wouldn't even need to fire a missile. They could just load it onto a boat and hand it over to someone in an undisclosed location.
The Middle East is sitting there, bristling with weapons and hate, and the only reason they can't attack Israel is because there is a nuclear imbalance. If both sides were nuclear powers, no one would want to use them and face the same in return, so it shifts back down to military might.
So, for that reason, a nuclear weapon in the hands of the Iranians would most certainly mean attacks on Israel. Non-nuclear attacks, mind you, but then what are you gonna do about it, huh? It's like fistfighting someone while their brother holds a gun on you, and your brother holds a gun on him. You're gonna be a lot less apt to disrespect the Marquis of Queensbury. In terms of standard combat of numbers and strength, Israel is at a disadvantage when dealing with the Arab world as a whole.