Beachcomber has it right actually.
The point is I feel that if you are going to put on a skirt and a wig and make up and call yourself rachel and go out with the girls and have a different 'girly' personality, adopt this silly lads/girls language and go to hen dos which you could never attend as your 'male' persona (rather than just happen to be wearing an item of clothing you like) what you are doing is making a determination that men and women are inherently different and separate.
A less extreme version is the idea of things being feminine or masculine and people having masculine and feminine sides, women being 'one of the lads' - drinking pints, laughing at sexist jokes, men being 'in touch with' their 'feminine sides' - doing the ironing, rather than people just being different. You create gender roles - women are to look sexy and do the cooking (heaven forbid a real woman look like gollum in a frock) and men are red-blooded and do sports.
Men who 'crossdress' buy so much into this sexist stereotyping fallacy that they feel they cannot just exist as a person with different attributes, they have to split their lives completely into 'male' and 'female' polarised personas. Hanging out with women - that's the female persona, playing sport - that's the male. The male persona is 'red blooded', the female goes out with 'the girls'. They simply cannot deal with people being people they have to have an outlet for the parts of them they consider female. They reduce both men and women to separate and mutually exclusive beings but as they are crossdressing rather than transgender they view the male persona still as the dominant one.
When expressing the female persona this is why they adopt wholeheartedly all the horrible sexist bullshit that has been pushed onto women because they equate womanhood with this crap, because whilst they see themselves as male and female (although with this duality and still with male dominance) they see women as no more than this superficial crap and they often believe what they are doing is loving women when they do this.
And yes it is offensive even on a basic level when a male fetishises tools partriarchy has used in order to oppress women. Yes it is depressing when women are still unable to face the day without make up and wreck their knees wearing high heels but women do it because they are under pressure from society. Men who do it through crossdressing are further imposing this ridiculous view of what womanhood should mean on women.