It is helpful to remember that Paul's letters are usually written to answer some very specific questions or to address specific situations in his churches. What is sometimes difficult is figuring out what the original question, accusation, or issue happened to be. In chapter 1 Paul seems to be defending his apostleship against unidentified opponents. There appear to be "false" teachers in the church turning people away from what Paul taught them (6-9). It seems from 10 that Paul is accused of being a "people pleaser". And from 11 to the end of the chapter (and on into chapter 2) there seems to be an issue with some suggesting that Paul was simply teaching "the precepts of humans" and didn't have the "divine" right to teach as he has taught.
At the heart of the discussion is an issue that no longer matters to the 21st century church. The issue for Paul's churches was whether or not a person had to become fully Jewish (in dress, circumcision and legal details) in order to become Christian. The "judaizer" party -- those arguing that one must comply to these elements -- is apparently at work in Galatia (as they were in Jerusalem and other places). In the modern church this is not a matter of contention, in fact, I would suggest we have gone a little too far from our Hebrew roots. All too often we attempt to read the New Testament (and especially the Gospel) as if it were delivered independent of its history. The key to understanding the life and teachings of Jesus are seen in looking back into the texts and traditions of the old. Now, having said that, it is clear that the "religious" practices are not carried forward. The dietary rules, the clothing, etc. are not carried into the new faith called The Way. And circumcision as a mark of belonging to the family is replaced with the water of baptism. We belong through our relationship with Jesus Christ and are marked with the water of baptism.
In short, we are free from the rules and restrictions of the old being necessary to please God and are now free to live fully and completely into our new relationship with the Son of God.