What is the reason of America's support of what is called moderate parties of Iran (such as mullah hassan rouhani)?
I am not sure if he said this: Ahmadinijad was stupid enbough to be a wolf in wolf's clothing, to expose his teeth and nails and alert the west. I can be a wolf in sheep's clothing. I have all the diplomatic and rhetoric skills to do so. , but Hassan Rouhani has two features: 1- anti-west. 2- pro-west (slight).
To see this refer to wikiquote:
1-The beautiful cry of 'Death to America' unites our nation.
2- What I truly wish is for moderation to return to the country. This is my only wish. Extremism pains me greatly. We have suffered many blows as a result of extremism.---The relationship between Iran and the United States is a complicated and difficult question. There is a chronic wound, which is difficult to heal. However, it is not impossible provided there is goodwill and mutual respect between the two countries.
The first is for 1995. the second is for 2013. Some in the US believe this is a gradual change, some believe this is a fraud. Those western media that support Hassan Rouhani are from the 1st group.
I find it unsurprising that the outlets mentioned would take such a position, due to the lack of realistic alternatives. It's a classic case of settling for the lesser evil. If the question is meant to imply that these media outlets are naively optimistic about what the likes of Rohani will do, I don't think that is necessarily the case.
A 2013 analysis for CNN by Majid Rafizadeh was widely quoted in Western media when Rohani became president.
Although Rohani argues for constructive interactions with other countries and although he supports applying a softer political tone – as opposed to the combative, controversial and provocative language that Mahmoud Ahmadinejad or other hardliners utilize – when dealing with the international community and regional state actors in regards to Syria, Rohani has not called for an overall sweeping shift in Iran's foreign policy.
I think the phrase in bold is the fundamental answer to the original question. While it is accepted that Rohani is not changing Iran's foreign policy, it doesn't follow that the US would be better off with someone like Ahmadinejad in power.