The conflict here is gender roles.
There are many theories on gender identity. Some people think that it exists, and that people can act masculine, feminine and others are genderless. Some cultures even believe in a third gender, someone who does not display masculine or feminine traits or display both.
Others do not believe that there is a such thing as a gender identity.
I would say that typically people who promote a gender identity tend to renforce the gender identity more than they deconstruct it, which is the purpose of believing there is a gender identity because it opens peoples' eyes up to say that is it possible to display characteristics of the opposite gender. I personally do not believe in gender roles.
That being the case, this issue looks quite silly. As it has been stated, the only reason this is an issue is because of society's views. To those who have stated that a stay at home father would never be acceptable in your household, look at that statement for a minute. Is it truly because you think a female's place is at home, or is it because the way your relationship is set up, the female is the member of a male/female partnership who chose that job, and the male of the same relationship simply prefers to work outside of the home?
Contraversally, you must also consider that there are families that exist in which there is not a female partner in a two way relationship. Homosexual couples may assign gender roles to each pair of the family, but in a male/male relationship there technically would be no female to stay at home, so then it is a matter of preference of the two people. It may be more difficult to imagine a female/female relationship, for there is no biological male to be the breadwinner, so it must be decided amongst the same sex couple who would like to do each job.
There is also the issue, that has been mentioned, of an unbalanced relationship. There are situations in which there should not be a stay at home parent and a parent working, for it makes child raising inherently unequal. If there was ever a cause for divorce amongst a couple who share the one parent works/ one parent stays at home relationship, it would be this. Biological sex is purely irrelevant when it comes to problems between a couple. The complaints are not 'I believe people who are in possesion of breasts an a vagina should take care of a child and a person in possesion of a penis should work', it is an arguement of societal beliefs.