Israel's enemies know Israel has nuclear weapons so no need to prove it to them but if it was made public the US would have no choice but to refuse to give Israel military aid as US law forbids the granting of military aid to nuclear powers outside the main 5.

Israel would be forced to chose between

Nuclear weapons which are the last resort weapon which is hoped will never be used and no military aid which Israel requires in order to keep its edge when it comes to conventional military capabilities unless it plans to spend much more of its own money to buy weaponry at market rates which will involve either raising taxes or borrowing more.
So better say nothing about nuclear capability and enjoy the best of both worlds

"Carter administration covered up clandestine Israeli nuclear test" does not tally with "Foreign Policy didn't point to a single smoking gun connecting Israel to the event and no official source has ever publicly confirmed that Israel has carried out a nuclear test".

hungry Israeli journos and ousted ex-this and that

Equal rights for men and women, when all Iran is allowed is a clandestine nuclear weapons program?