This is just conjecture, but maybe in Spanish, saying that something IS another thing is equal to applying that "another thing" as an adjective before the noun. For example, the phrase "the bed that is red" has the same meaning as the phrase "the red bed." Maybe saying "My wife is doctor" (in Spanish) is similar to saying "My doctor wife," with "doctor" being an adjective. This seems like an abstract concept, and, like I said, this is just conjecture. I might be completely wrong! I hope this helped though. :)
I object to "my lady is a doctor" not being an acceptable translation as with both English and Spanish referring to your woman/lady implies ownership (i.e. marriage) and similarly in Spanish the Mi mujer (mujer meaning woman/lady) also being an acceptable replacement for esposa to mean wife.
A lot of times when you're referring to someone's profession in Spanish, the article ("a") gets dropped. "Mi padre es granjero" means "My father is a farmer." It's just a little idiosyncracy of the language. I don't think you have to drop the article, but if you don't, you'll sound a little awkward and like a foreigner.
I have been watching the Spanish drama "I know who you are" on BBC4 and each time "my wife" has been said, they have said "mi mujer". That is the common way the Spanish refer to their wives. We are trying to learn to speak Spanish so we should follow what the Spanish say surely.
'My woman' is said even in English, moral discussions aside it is not hard to understand it to mean wife or girlfriend.
As for the article, you don't use them when referring to occupation in Spanish. Comparitivly, native Spanish speakers learning English often omit the article when speaking English, and that is a mistake. Don't waste your time trying to understand why...Different languages just evolved in different ways, and when translating, you impose your own language's grammar.
I don't know about Spanish, but I don't agree that it sounds patriarchal in English. It's the opposite of "my man," which I hear more often anyways. Men and women alike feel possessive over their spouses and special friends, and what you call patriarchal, I call romantic or cute.
I read the comments but perhaps I dont fully understand about there being no article used with doctor. It seems that, in Spanish, articles are used more frequently than in English. I expected this one to need the article with doctor. : ( Anyone else confused about this? Perhaps some input from native Spanish speakers? Thanks!
When I was growing up, it was common to hear people refer to their common-law wives our girlfriends as their woman, but I have never heard anybody refer to somebody they're married to as their woman. But we can't judge another language or culture by our standards. Maybe mujer is just another name for wife in some countries. It just sounds vulgar when we translate it as 'woman,' and it is used in a context in which we find 'woman' unacceptable