Israel's Nuclear Closet

This is one of those things that to someone coming across the debate for the first time seems utterly mysterious. Why should the United States have to pretend that Israel has no nuclear weapons when everybody knows it does? I've been reading the usual suspects on this for insight and ... not much luck. From the point of view of, say, Iran, it seems perfectly reasonable for them to ask why they can't have a couple of nukes when their chief regional rival, Israel, has scores. And how do you have an adult conversation with a country like Iran when we are required to keep lying about the regional arms situation ... because the Israelis want to have their nuclear cake and eat it too?

Since I'm a believer in nuclear deterrence - it worked pretty well with the Soviets - you could even argue that a formal, MAD-style Iran-Israel stand-off, like the US-USSR stand-off, would help keep the Middle East from the apocalypse the way the world was from the 1940s to the 1990s. But what do I know? Even hinting at some basic public honesty on this matter will presumably unleash another wave of accusations that I'm a nineteenth century Jew-baiter. But isn't it obvious that Israel would be smarter to develop a more normal relationship with the US as a sounder basis for its long-term security than the cloying and unhealthy clusterfuck we currently have? This gets it about right to me:

Why couldn’t Israel just declare that it is a nuclear power?
It is one of those secrets that everyone knows about but nobody publicly acknowledges. Expect the smirking President of Iran which gives him credibility he certainly does not deserve. Israel should just come clean about its nukes and also its intent to use them on anyone desiring to erase Israel off the face of the earth (as some adversaries dramatically like to put it). It would make certain negotiations a lot easier. Of course, it would also force us to acknowledge our double standards on why only certain select countries (that we like) deserve to have nukes. But I think that would also be a positive outcome.

Maybe I'm missing something here. I'm not versed in the history of this. But it begins to look once again as if Israel is privileged not as normal allies are privileged, but as a very special case which has the right to have nukes, while demanding none of its neighbors does, and that we cannot even say it has such a capacity; that it has the right to launch wars and threaten wars against its neighbors, but its neighbors have no right to do the same, and so on. It doesn't seem healthy to me - for the US or for Israel.