Because if you say anything (however justified) about Isreal you get publicly lynched as an "anti-semite" faster than you can blink.
That's certainly part of their political and diplomatic arsenal.
There's such a thing in international politics as strategic ambiguity - you don't clarify your position because you benefit from the uncertainty overall. It's generally a sign you have some serious conflicts of interest. In this case, in addition to reasons of military secrecy, Israel are afraid that openly declaring nuclear weapon capability would (a) cause the Arab states or Iran to withdraw from the nuclear non-proliferation treaty (b) and/or pursue their own nuclear weapons for self-defence or deterrence against a first strike by Israel. That's a hell of a downside so Israel don't openly declare their nuclear capability, but they throw enough hints to make sure decision-makers in those countries get the message.
I struggle a bit with this, even though it is the orthodox. Maybe I've got to go back and read my Freedman and Schelling again, and this goes to the DPRK situation again as well.
You're saying that if Israel is a declared nuke state that will cause Iran to go nuke. The ambiguity now means that Iran is unsure and therefore isn't forced to do so. This is where I don't think that works:
#1 - Iran has had a nuke program for decades with Israel and the US being primary targets with KSA likely secondary. This didn't take Israel being a declared nuclear state
#2 - It's pretty much conventional knowledge that Israel is a nuclear state, Mordechai Vanunu and others are on the record, etc. etc. Everyone assumes that Israel is a nuke state, it's the working assumption. So what difference does an open declaration mean? Same question for DPRK. They are so close to having a weaponisable device and they have the ability to launch a multistage ICBM. Do we feel safe making the assumption that they haven't miniturised it? Do we feel safe that they can't throw a flatter trajectory ICBM with a survivable warhead? Who's willing to bet their population on those gambles? No one, that's one of the reasons that THAAD is in place, why the region is full of Aegis, etc. etc. Does it take a declaration and recognition to precipitate a response? No.
#-3 and that brings up #3. If Iran even thinks it's possible that Israel has nukes they have to assume they do, even if they declare they are not (as in they are not playing the ambiguity card) because the risk of getting that assumption wrong is an existential one. I guess this falls into the capabilities rather than intent area. If you think your adversary has the capability you don't care what they say, you take measures to protect yourself. Just as the US, Japan, ROK, etc. are doing against DPRK and just as Iran was doing against Israel, etc.
Is there a reason Israel gets to have their undeclared program? Same reason why India and PAkistan get to have their declared program without being part of the NPT - because whaddaya gonna do?
India and Pakistan don't threaten anyone but each other. Yes, India and China stare down the missile at each other but there is little risk of nuclear war between them, it's just not a thing, at the moment. Nobody feels threatened by them and the cost to remove that capability from them (in case their intent changes) is far too costly. The bigger powers - US, Russia, UK, France, China etc. get along with India, PAkistan and Israel all well enough that trying to coerce them into losing their nukes would cost more than it would gain now that they have them and the means to deliver them. Once countries have nukes it's very hard to persuade them to lose them - countries get nukes specifically so they CAN'T be coerced into doing things they don't want to do. That's what nukes are.