its because the US is an 'empire'.

'Avoid foreign entanglements' was George Washingtons advice.

The road to empire and to hell, is paved with good intentions.
Woodrow Wilson whose campaign theme was 'he kept us out of the war'
got the US into WWI to 'keep the world safe for Democracy'
(never mind what the British colonials in India and Egypt must have thought of that)

Kennedy said 'if the South Vietnamese want a revolution they should do it themselves like we did'
Johnson who opposed sending American boys to Southeast Asia to do a job that the Asians should be doing themselves - turned right around
and sent them in .
Somehow 'fighting for democracy' and 'we'll bomb them to the stone age ' seem to be contradictory values.

Bush 'the decider' who didnt believe in nation building, and went ahead did it anyway.

with regard to the question:
Why is it such a big deal that Iran might develop nuclear weapons.
Mainly because they (like Korea) have realized that this would prevent the US from trying to topple their regime.
The main threat is really to Americas superpower status.
Its due for a decline anyway as all empires do.