(Like this is about Fauxborn Murphy specifically, but it pretty much applies to regular Murphy too.)

Murphy sees being the Divine Maiden, the Divine Mother, as a curse and becoming a human sacrifice. She's not wrong to do so, with the amount of people that have been discarded for failing to live up to the role. So she wants Miryam to say "I love you," to be able to call Miryam her mother, because that means Murphy is a person, not a tool, to Miryam.

On the other end with Miryam... Miryam was taught over and over, had it literally crushed into her, that you do not put anything before God. That you sacrifice your family to God without hesitation. So for her, to call Murphy her daughter would be resigning her to be the sacrifice Murphy fears she is. For Miryam, the best way she can show her love is put Murphy on the same level AS God, as something Divine, because that's what Miryam is supposed to value most in her life as High Priestess of Lemuria.

Nearly forgot abt Murphy’s bday… here’s a quick sketch I put up in an hour!