Analytic phonics focuses more on teaching whole words first and then analyzing on the constituents parts which made up the word whereas synthetic phonics focuses on the sounds of letters and letter combinations are taught first and later the method is taught to form complete words.
I think that cringe means that a response to embarrasement. But right now in this text I think this word means that they didn't want that to happen. Or they thought that was not good. Hopefully it's right. I mean that's just my opinion. :D