Sorry I am a mother, and this is the mens room, but the title grabbed my attention.
Many years ago, before kids, my dh and I was out having drinks with another couple, the woman was a social worker. She was advocating that men should not bathe or change their daughters unless in the presence of their mother. And fathers should not co-sleep with their daughters unless the mum was also there.
I dont know what special circumstances her job brought her into contact with, but I found this extremely odd and sad. It totally baffled me.
I think you need to talk to your fiance about his views. You need to establish whether he is just lazy and using this as an excuse, or if he has some worries that needs adressing. Why did he come to this conclusion? Did his ex (I assume he has an ex as you mention he had no problems with changing sons and you and him only have a dd together) refuse him to care for his girl? Is it something related to his culture?
But I think you must not address it from the perspective of you needing help with babycare, but out of concern for him, your dd and the closeness issue. Not that you needing help with babycare is not important, but I dont think that angle is going to help him open up about his concerns.
My dh, is very reluctant to change his sons nappy, simply because he doesnt like it. So it is my job, my dh is honest about not wanting to do it. He does other things, so it is not like I am the only one doing "baby stuff". It could be as simple as your fiance not really liking to clean up poo, and not willing to admit it.
Sorry, I do go on, dont I?