The deal was not perfect. It allowed Iran to enrich uranium - a key step in building nuclear weapons - under temporary conditions, allowing critics to argue that Iran was buying time to launch a nuclear weapons programme in future.
Israeli Prime Minister Benjamin Netanyahu attempted to produce the smoking gun on this issue last week, but his trove of stolen documents merely showed that Iran was secretly aiming to build nuclear weapons up until 2003 - not that it had breached the 2015 deal.
While Netanhayu's pitch to Trump may have worked, his argument was undermined by his own military chiefs, who have said the deal is working and has delayed Iran's nuclear capability by 10 to 15 years. Others fear that pulling out will weaken Iran's relatively moderate civilian Government and embolden the hardliners.
It remains to be seen whether Trump can kill the agreement single-handedly. Britain, France and Germany yesterday expressed "regret and concern" and pledged their continued commitment.
Europe did $25 billion of trade with Iran last year, more than 10 times the US figure, and Iran has hinted that it could still be interested if the benefits are great enough. However this could be difficult in practice, because nearly all global transactions at some point pass through the US financial system, which will be off limits to Iran.
Trump's short-sighted motivation for the move is not limited to revenge on Obama. He is also playing to his domestic base, especially evangelical Christians who see the Middle East in ideological terms, with America and Israel in God's corner and Iran as the face of evil. Others around him have more disturbing ambitions.
New Secretary of State Mike Pompeo and national security adviser John Bolton have advocated a bombing campaign to achieve regime change and new lawyer Rudy Guiliani is reported to have taken large sums of money from Muhjahideen-e-Khalq, an exiled Iranian resistance group once listed by the State Department as a terrorist group. If US-forced regime change is the real goal here, things could get even worse.