Hysterical!
My grandfather used to read to me pretty every day, from when I was a toddler throughout the preschool years.
My mother tried to start me on the basics of reading during the summer before 1st grade (back when the only thing you learned in K was how to write your name). I don't know if she was worried for me (I was skipping K). I point blank refused to go past lesson 2 in the book. I also refused to learn to count past 10 when my grandmother tried to teach me the weekend before school started. I clearly remember feeling very resentful about it all, thinking "that's what I am going to big kids' school to learn, why are you bugging me???".
In December I was reading the newspaper to my grandfather. A few months later our reading sessions were gone. I had moved past the need, but... I can understand a child deciding to pretend not to be able to read (or refusing to learn) in order to keep the reading-together time.
Shellymos, if you want to push it, maybe stress the fact that her reading time with you will remain as is, and set up a separate time for her to learn how to read/buddy read with you/read independently?