As far as I know, FGM is Not practiced by the SHIAS,who are 90% of Muslims in Iran,but here is the info on why the SUNNIS do it:
APPROVED IN THE SAYINGS ( hadiths) of MOHAMMED
FGM is also called FEMALE CIRCUMCISION is Not Obligatory but it is PERMITTED in 6 SEPARATE sayings of Mohammed .
Here they are( from WIKILSAM )
The fitrah is five things, including circumcision
Note that the RULE of HADITH dictate that if it is not mentioned specifically or if the pronouns do not point to a certain gender,
then the hadith is VALID for BOTH SEXES. Hence, the following hadiths are APPLICABLE for both MEN and WOMEN.
(Abu Hurayrah said: I heard the PROPHET (peace and blessings of Allaah be upon him) say: “The fitrah is five things – or five things are part of the fitrah –
shaving the pubes, trimming the moustache, cutting the nails and plucking the armpit hairs.)
(Bukhari 5891 and ALSO in Muslim 527)
A preservation of honor for women
(Abu al- Malih ibn `Usama’s father relates that the PROPHET said: “CIRCUMCISION is a LAW for MEN and a PRESERVATION of HONOR for WOMEN.”)
(Ahmad Ibn Hanbal 5:75; Abu Dawud, Adab 167.)
Do not cut “severely”
Note that the judgement concerning what is severe is relative.
(Narrated Umm Atiyyah al-Ansariyyah: A woman used to perform circumcision in Medina.
The PROPHET (peace be upon him) said to her: “Do NOT CUT SEVERELY as that is better for a woman and more desirable for a husband.”)
(Sunan Abu Dawud 41:5251)
When the circumcised parts touch each other
(Abu Musa reported: There cropped up a difference of opinion between a group of Muhajirs (Emigrants and a group of Ansar (Helpers) (and the point of dispute was) that the Ansar said: The bath (because of sexual intercourse) becomes obligatory only-when the semen spurts out or ejaculates.
But the Muhajirs said: When a man has sexual intercourse (with the woman), a bath becomes obligatory (no matter whether or not there is seminal emission or ejaculation). Abu Musa said: Well, I satisfy you on this (issue).
He (Abu Musa, the narrator) said: I got up (and went) to ‘A’isha and sought her permission and it was granted, and I said to her: 0 Mother, or Mother of the Faithful, I want to ask you about a matter on which I feel shy.
She said: Don’t feel shy of asking me about a thing which you can ask your mother, who gave you birth, for I am too your mother.
Upon this I said: What makes a bath obligatory for a person? She replied: You have come across one well informed! The Messenger of Allah (may peace be upon him) said: When anyone sits amidst four parts (of the woman) and the CIRCUMCISED PARTS
TOUCH EACH OTHER a bath becomes obligatory.)
(Sahih Muslim 3:684)