The short answer: The world oil market.
In 1986, the US waged an undeclared proxy naval war to deter Iran from attacking oil tankers in the Persian Gulf. The US won of course and Iran lacked any effective riposte. This US operation played a decisive role in compelling Iran to accept peace in the Iran-Iraq war.
And it may have prompted Iranian leaders to decide: We need an effective counter-deterrent against the US. The US would have been much more reluctant to protect Kuwaiti tankers against a nuclear Iran. An Iranian nuclear bomb would act as a “Keep Out” sign to frighten the US away from a now truly Persian Gulf.
Justin notes that the U.S. would hardly be standing alone in its disquiet if the Iranians started randomly blowing up Kuwaiti oil tankers, and it's really not clear what a small Iranian nuclear arsenal would let them get away with in the face of what would be uniform hostility from every major power and every country in the region. But beyond that, why is Iran blowing up these Kuwait tankers? In the previous Gulf go-round what happened was that Saddam Hussein launched an unprovoked invasion of Iran, the invasion went poorly, the Iranians launched a counter-offensive, then the U.S. and the Gulf states started organizing to help Saddam.
Whatever you think of that series of events, it's certainly not evidence that Iran has long-standing ambitions to mount unprovoked attacks on the world's oil distribution networks. Most likely, what Iran would like to do is sell oil to oil-importing nations and use the resulting funds to buy stuff.