My DD did something similar up to early age 5, wherein we knew she could read from all these other interactions, but she refused to read aloud to us. No pressure - she was still in pre-K at the time, so there was no necessity. In my school we didn't do reading groups until 1st grade, so she had two full years before this could even be considered an issue.
Looking to motivate her, I praised her for all the ways she was ahead of me at that same age, except one - because I had begun reading aloud to my mother at age 4. DD read a book she had never seen before aloud to her mother the next week. Before long, her pre-K teacher had turned story time over to DD.
We chalked it up to anxiety and perfectionism. She was afraid to try it because she might stumble or get some things wrong.
Probably the most important and useful thing you could do right now is to stop worrying about it. If you're pressing her on this, it could feed into her anxiety.
Sia's point is also cogent. Apart from telling her that you'll keep reading to her until she doesn't want it anymore, you could also segue into independent reading by making it mutually-participatory... take turns. This could be done at first by assigning your DD some of the dialog voices, which can be a lot of fun.
