As society progresses it becomes (or has become) more tolerant of peoples personal preferences.
Not so long ago if you was homosexual you would be branded as insane (criminally insane in fact) and most likely be chemically castrated (just look at the terrible way Alan Turing was treated).
Not so long ago if you wore ripped jeans and Mohawk with rings in your face you would probably be institutionalised or told you had been possessed by the devil. If you announced you had been born in the wrong body/gender, something similar would probably happen.
People in the west can afford to be far more tolerant of what was once deemed unacceptably different as wealth, personal freedom and overall life security has increased. In western society a person telling you they feel they are a woman trapped in a mans body is highly unlikely to have any effect upon yourself.
In a less developed country or say perhaps a small tribe in an amazon rain forrest, such a statement may cause a great deal of alarm, is the person a man or a woman? will they be able to hunt, fight, protect the village from wild animals and intruders? it throws a whole other set of concerns into the mix.
People have more time nowadays to think about themselves and how they feel and how they want their lives to be, in the past (and perhaps in developing nations) people had to think more about their family and 'tribe' as a whole rather than their own personal needs and wants.
Personally I think its a good think that humanity is coming to the point where people can choose what they want to be (if indeed it is any choice at all), and if somebody says they feel they are a man/woman trapped in the wrong body, well that is no business of mine and if it makes them happy to change into the person they want to be, then all the better.
It does make me think of a South Park episode however when Randy feels he is a Dolphin born into the body of a man (very silly I know
), and just how long it will take before gene manipulation will allow animal splicing with our own. But again, that's a whole different discussion