I think I just couldn't. When you have kids, your whole life is altered. You speak differently (fewer swears and "stupid"'s and "hate"'s), you watch different TV shows (the Mickey Mouse Clubhouse theme song is permanently stuck in my brain) and eat different foods (what they like + what they need to like = dinner). I felt like giving up "my" books was a step too far.
We read picture books and bedtime stories and read alouds, but my reading for pleasure time needed to be my own.
The YA and middle-grade genres are full of gems. But if you're reading a gem because you feel obligated, it changes the experience. Also, I often felt frustrated. I would love a book and recommend it to my kids and they would say, "Cool," and then go read what they wanted.
I occasionally pick up a book that one of my kids recommends to me and have stopped trying to give them so many of my favorites. We spend exorbitant amounts of time at the library and bookstore and they don't really need another person trying to hand them more books. I love the freedom of picking what I want to read next without any coercion and it's only fair to give them the same experience.
We talk about books all the time and I've also realized, our tastes in books are not the same. And that's ok. I was secretly hoping that all of my children would be born with a passion for Austen and Dickens and Hemingway, just like me. They would love a cozy mystery and be completely turned off by science fiction. That did not happen, and the world is better because of it. Making that realization has freed me and the kids to develop our own literary preferences. We are individuals after all.
Allowing myself to read the books that attract my attention makes me a much more voracious reader. The same is true of my kids.
I still haven't mastered the art of not finishing books I can't stand, but at least I've made this step in the right direction.