But if the US and Israel, and GB and France can have nukes, then so can Iran. Or do these countries think they have a god-given right to bully otehr countriies as tehy please?
moral relativism 
Iran signed the NPT so they can't have nukes.
If they want nukes they must leave the NPT.
Saying that you're doing it for peaceful purposes whileeveloping nuclear 'power' in secret (while the NPT stipulates that nations have the right to develop nuclear power) is not a way to make others trust you. Declining a deal whereby another nations would provide (sell) you with the enriched uranium you need is not a sign of wanting to develop nuclear power for peaceful purposes only, especailly if you consider that the only nations doing uranium enrichment are all nuclear powers. Having a president that states that Israel should be wiped off the map and states that the holocaust is a european-zionist conspiracy is also not a good way to engender trust, especially coupled to the fact that the country of said president is notorious for sponsering terrorist groups that strike against Israel.
Israel (iirc) developed its nukes (assuming they have them since it is still not confirmed
) before the NPT so they're entitled to have them. India and Pakistan were not, iirc, signatories to the NPT so they're entitled to have them.
We're the West, that's why! 
i do hope that's sarcasm, otherwise, Nuclear weapons have this allure of a big shiny saber to rattle at your enemies, like 'invade me country, and i'll vaporise you with a cleansing atomic fire" or some such ****e, this is what kept the cold war like it was, mutually assured destruction, both east and west were rattling their own nuclear weapons like babies with a rattle.. the only difference between the west, and those countries that are newly joining "the nuclear club" is that the US, russia, GB, france, etc have had the funds to actively test them, and accurately measure their destructive force, that, and they'd most likely be less trigger happy than, say the US..
as i see it, the big western countries want to keep the status quo of their own impressive arsenal of WMD's, when everybody has one, then the mutally assured destruction factor would kick in for all involved, they nuke us, we nuke them, somebody else nukes us.... mind you, what happens when everybody has 'The bomb" ?... that's right, somebody will up and redefine the term, and come up with something just as cataclysmic.
long story short, nuclear = power, no matter how you use it, for electricity, pretty much literal, for weapons, political power, or ire, depending on which end of it you're on.
given how the UN was pretty much built around the global threat of nuclear weapons during the post-ww2 years & the cold war, it's rather unfortunate that these days, they haven't got much clout beyond the odd economical embargo.