OK first two facts: 1. Israel fears its neighbours might start another war that could be costly to Israel (as well). It sees its nukes as a last resort guarantee for the continued existence of Israel. It is not conceivable that Israel will get rid of its nukes in any near future. 2. Israeli neighbours fear both Israel's nuclear capability and its superiority in regular arms, as they see both as threats to their own countries. The logical result is that Israel's neighbours will try to protect themselves against the perceived threat, most likely by acquiring their own nukes, thereby levelling the playing-field. This is a development that nobody wishes, Israel least of all. Therefore Israel needs to alleviate the fears of its neighbours. Thereby lessening their eagerness to acquire nuclear capability. It is entirely possible for former enemies to live side by side in peace, even with an imbalance in military strength. Just look at France and Germany. But it requires peace and it requires confidence building gestures by the stronger party, otherwise the result is just an arms race. The biggest question is of course Palestine, but in the meantime: what's so scary about the NPT? If Israeli abided by the almost universal treaty and made its nuclear program slightly more transparent it would go a long way toward reducing its neighbours anxiety about the program. What exactly are the downsides? The NPT doesn't really require any disarmament, and it is highly unlikely that the other 5 states will get rid of all their nukes any time soon, if ever. In short, Israel could retain its nukes and at the same time give some assurance of peaceful intentions to its neighbours. Not to mention that Bibi can complain about Iran without sounding like a total hypocrite.
Knesset approves 2015-16 state budget in first reading (Haaretz)
from the article: Report: IAEA to discuss Israel's nuclear activities for first time