Mr Amer politely refuses, saying for a Muslim man to shake a woman's hand is contrary to his religion's teachings.
I am not offended; I have struck this before at a previous interview at Dunedin's al-Huda Mosque.
I assume it is because I do not share his faith.
Later, Mr Amer explains not shaking a woman's hand is nothing to do with me not being a Muslim - Muslim men and women do not shake each other's hands either.
Instead, not taking my hand is a sign of respect for me and my gender, he says.
There are exceptions though.
As a trainee doctor, Mr Amer says he has no problem shaking a female patient's hand, or examining her.
Gender separation is a given for Muslims, I learn.
They do not hug a person of the opposite gender who is not a family member.
Or socialise with the opposite sex unless at family occasions. Or go on dates before marriage.
And despite being in a university city which takes co-ed living for granted, they definitely do not live in mixed-gender residential colleges or flats.
When arranging the interview I had asked if I could talk to a female Muslim about living and studying in Dunedin.
As the interview begins, Mr Amer says he was unable to find a woman prepared to be interviewed.
As the interview ends, the true situation is revealed.
I am preparing to leave when two smiling young women, Ahya Hasni and Afila Omar, emerge from the shadows and tell me they are happy to talk.
From what I have learnt from the men, I realise my expectation that I would interview men and women together was inappropriate but they had not wanted to tell me that.
Even at Islam's religious services the genders are strictly separated.
Men and women pray in separate rooms and study groups.
Social activities are also segregated.
In Dunedin, some Muslim women go to the Mosque for Friday afternoon prayers and stay to listen to the sermon.
Ms Hasni and Ms Omar say that took some getting used to, as the women in their native Malaysia carry out their Friday prayers at home.
Their Sunday swimming sessions are in private; only Muslim women attend and they are watched over by a female lifeguard.
They attend camps and social events organised by the Mosque's sisters' committee.
No men are present.
"We can have a social life. We're allowed to have fun. It's just there are no men around," Ms Omar says.
The extent of the gender separation is apparent when the women tell me that despite living in Dunedin for two years, they do not really know many Muslim men, apart from those in their medical school classes.
They do not question it - it is what they have been used to all their lives.
Such strict gender segregation begs the obvious question: How do young Muslim men and young Muslim women fall in love and marry?They follow the traditional practices, the students say.
Families talk among themselves, parents talk some more with their children and suitable matches are identified.
The intending groom approaches the prospective bride's family to see if marriage is possible and to meet her with chaperones.
It is not all archaic, the women say. Modern Muslim women can decline.
Ms Omar, who like her friend is unmarried, says she does not mind if her parents suggest a husband for her.
"But they need to respect my right to say no."
Men and women with their eye on a potential marriage partner can hurry the process along, the pair say with a giggle.
This is done by pointing out a possible match to siblings or older relatives and leaving it to them to pass the suggestion on to the prospective bride or groom's parents.
Mr Amer, who is not married, says it can take five or six attempts at matchmaking before a man and woman agree to marry.
Mr Noorebad married two years ago.
His wife, Kawaba, was a relative from his native Afghanistan whom he had met at several family functions while they were growing up.
He brought her to New Zealand under this country's cultural arranged marriage policy for immigrants.
It seems incongruous that Muslim parents would allow their daughters to leave home and study alone in another country, but Ms Hasni and Ms Omar say their parents had no qualms, apart from the usual parental concerns about where their daughters would be living and who would be looking out for them.
Despite what many non-Muslims believe, Muslim women are encouraged to be educated and to work, they say.
Islam teaches that men are the leaders of their family, but it does not teach that women are inferior.
"We have different rules, but the rules don't put one gender above or below the other," Ms Hasni says.
Children are an expected and welcome consequence of marriage, and Muslim parents work together to raise their children and provide for their their families.
And, adds Ms Omar, Muslim husbands are expected to do their share of the housework.