My cat bit me out of nowhere while I was petting her. She was purring right before.

This is one of the most common things I hear, and I understand why it feels so confusing because it seems like a contradiction. Purring and biting in the same moment. But what is happening is not a contradiction. Your cat was communicating the whole time. The signals were just very small and easy to miss, especially when you are focused on how nice the moment feels.

Cats have a threshold for touch that varies by individual, by body location, by time of day, and by how much contact they have already had. Purring does not always mean contentment in the way we tend to read it. Cats also purr when they are overstimulated or trying to manage their own state. By the time she bit, she had likely been sending signals for a few seconds, maybe longer: a slight tail flick, a small shift in body position, a change in the rhythm of her breathing or purring. These are easy to miss if you do not know what to look for.

The good news is that this is very workable. Learning her specific pre-bite signals, shortening petting sessions before she reaches threshold, and letting her initiate contact more often are the first steps. If you want to go through her specific patterns and history, including where she tolerates being touched and where she does not, the Work With Me assessment is a good place to map that out properly.