First of all, we should note that Iran claims that it is not building a weapons program but rather is only building a peaceful program for nuclear power generation. Therefore, Iran is not officially wanting to be allowed to do this.
To argue that Iran should be allowed to do this, you should argue that there is a double standard at work in the world. You should argue that there is no objective reason why a country like the United States or a country like Russia should be allowed to have nuclear weapons while Iran is not allowed to. You should reject the notion that countries that have nuclear weapons are somehow more mature and more able to handle having such weapons. You should also point out that such states as Israel, India, and Pakistan all have nuclear weapons and are allowed to do so because they did not sign the Nuclear Non-Proliferation Treaty.
Your argument, then, should be based on equity. It should be based on the idea that there is no fair way to say that some countries ought to be allowed nuclear weapons while others may not have them.