The arguments that Iran ought not to be allowed to build a bomb are of several sorts, a similar to those which were applied to Saddam Hussein prior to the invasion. First there's the standard line that proliferation of any kind is to be avoided. A second argument is that Iran possessing a nuclear weapon would allow a "nuclear umbrella" and would galvanize anti-western forces throughout the region. This strikes me as overblown. It seems unlikely to the extreme that Iran's nuclear umbrella would ever extend to proxy forces, nor does it seem to me that a nuclear weapon would put Iran in any particular good place from a strategic point of view. Most countries in the region either are under US protection or possess their own arsenals. The only gain Iran might have from their weapons would be deterrence, which doesn't seem much of an issue unless we are contemplating the invasion of Iran.
Stephen Walt has a lengthy post wherein he considers the possible effects of an Iranian bomb.
The key point to remember is that a decision to build a bomb involves some complex cost-benefit calculations, and Iran's acquisition of a nuclear weapon would not necessarily lead any of its neighbors to decide that their best course is to follow suit. One reason they might hold back is simply the recognition that getting a bomb would not enhance Iran's influence as much as is sometimes claimed. China did not suddenly become a more influential power when it tested a bomb in 1964; its rise to true great power status came when it began to modernize its economy in the l980s. Getting a bomb may have reinforced Israel's "existential security" (which is why Ben Gurion wanted one), but having a couple of hundred nuclear weapons doesn’t enable them to blackmail the Palestinians or the other Arab states into doing whatever Jerusalem wants. Similarly, North Korea has hardly any influence in world affairs despite its recent entry into the nuclear club; the only thing that that Pyongyang can do with its weapon is discourage others from putting too much pressure on them. Americans really should understand this: we have several thousand nuclear weapons and we have a tough enough time getting other states -- even rather weak ones -- to do what we want. The same would be true for a nuclear Iran: it could not blackmail anyone because the threat would not be credible, and even nearby states might find it easier to adjust to than we sometimes think .This strikes me as pretty sound. Iranian nuclear weapons would obviously not have a positive effect on the security in the region, but there negative effects are clearly massively over-hyped.
The final case is that a nuclear bomb represents a sort of final solution. This school of though points out the the USSR and Maoist China were fundamentally rational adversaries, whereas sees Mahmoud Ahmadinejad and the ruling ayatollahs (the difference between the two is often brushed over) are motivated by Millenarian beliefs and therefore fundamentally irrational. Under this theory, as soon as Iran achieves weaponization, they will destroy the state of Israel.
On its face, this seems completely reasonable, but in fact it seems very overblown. If Iran is so irrational, one would probably see it manifested in their actions, yet this doesn't seem to me to be the case. Iran is happy to increase its influence by selling weapons and political support to anti-Israeli terrorist militias, but they haven't had Revolutionary Guards fighting on the the front lines against Israel. A fundamentally irrational regime is generally manifests some way in its actions. Idi Amin and the Pol Pot both led fundamentally irrational regimes, but it was easy to tell how insane there regimes were, and because of their irrational actions, these regimes were removed from power. The case that Iran is irrational is based on no action in particular, rather it is based on speculation and key misreading of statements by the Iranian president. Though proponents of the irrationality view tend to contrast this with the USSR and Red China, they conveniently forget that when we faced these countries, they were considered just as irrational as we now say Iran is. Later we'll be contrasting rational Iran with the suppoed irrationality of whatever future adversary we face.
No power would welcome an Iranian bomb, and no one is arguing that Iranian nuclearization is a positive development. I would say, though, that overheated predictions of apocalyptic scenarios is no help to the dialogue.