There is no valid non-military reason to enrich uranium beyond the 20% that is the threshold to be considered highly enriched.
Highly enriched uranium (HEU has been historically used for several non-weapons applications: nuclear submarines, some types of civilian nuclear reactors, some types of isotopes for medical applications, and even satellites. However, the entire world has essentially agreed to eliminate the need for HEU in those applications.
For example, outside of a German FRM-II research reactor that has received massive criticism for continuing to use HEU, no new HEU-fueled civilian research reactors with a power level of more than 1 MW have been built in Western countries since the early 1980s. There is no reason to build such a reactor today.
The US Navy has been researching how to phase out the use of HEU for its nuclear submarines. France and China's nuclear submarines use low-enriched uranium. Yet Iran has floated the idea of building a nuclear submarine using HEU.
There is no technical reason why medical applications that still use HEU could not use LEU, meaning that HEU is not a "need" for any country's medical applications.
If Iran is insisting on enriching uranium to 60%, it is not for any legitimate purpose.
The problem is not only Iran building a nuclear weapon.
A simple nuclear weapon in the kiloton range—likely to be delivered by ship or van or assembled on site— is well within the capabilities of technically unsophisticated states, subnational groups, and international terrorist organizations such as al Qaida. The IAEA defines a "significant quantity" of fissile material as the amount required to make a first-generation Nagasaki-type implosion bomb: 8 kg for plutonium or 25 kg of U-235 contained in HEU. Modern nuclear weapons may require as little as 1 to 3 kg of plutonium or 5 to 10 kg of HEU.HEU may be the preferred nuclear weapon material for terrorists for other reasons as well. Uranium metal can be handled relatively safely by hand and the low radiation it emits is easily hidden by even modest shielding, making smuggling extremely difficult to detect. Sixty kilograms of weapons-grade HEU could easily fit into a five-liter container.In 2002, the US National Research Council warned that the inavailability of HEU was the "primary impediment" to the development of a terrorist bomb, and there is abundant evidence that terrorist groups have been trying aggressively to obtain nuclear materials.
Iran could smuggle the HEU to Hezbollah, which could attempt to bring a simple bomb to Israel by tunnel or boat.
In short, while the entire world is trying to reduce the use of HEU and finding ways to dispose of it safely, Iran is openly threatening to manufacture more HEU which has no legitimate purpose nowadays.