I live in a very atheist area where anything that modern 'science' says is taken as the absolute truth 100% of the time, which is no different to being indoctrinated into a religion. Science has become a new religion since most of what they come out with is not even observable, let alone testable and repeatable. I don't subscribe to any particular religion as I think they're all corrupt to a certain extent but I do believe there was a creator and I definitely do question the age of the earth.

There are lots of flaws with the methods like you said, if you want a good but short book I'd recommend reading 'thousands not billions' which was written by a Christian author and highlights the many flaws with the dating methods.