"How can she say she didn't like having sex with you and then ask you for sex all the time?" This too baffles me...but as you and Bttrfly have pointed out, the first time I said no was when I felt empowered...and saying no every subsequent time has been easier and easier...but yes, it still pushes my buttons...and she knows it.
If I were to guess ... in MLC they tend to simply transfer the 'love' they once had for us towards the OP, but what they have difficulty doing is transferring all those shared memories and moments. Read enough and you will find several attempts to diffuse this ... the MLCr will take the OP to 'our spots' in an attempt to replace us and our memories with new ones.
I would take an educated guess that she desires sex just to confirm there is no connection between the two of you and to validate all her choices that have lead up to this much like taking the OP to your favorite restaurant or park.