12 I plead with you, brothers and sisters, become like me, for I became like you. You did me no wrong. 13 As you know, it was because of an illness that I first preached the gospel to you, 14 and even though my illness was a trial to you, you did not treat me with contempt or scorn. Instead, you welcomed me as if I were an angel of God, as if I were Christ Jesus himself. 15 Where, then, is your blessing of me now? I can testify that, if you could have done so, you would have torn out your eyes and given them to me. 16 Have I now become your enemy by telling you the truth?
17 Those people are zealous to win you over, but for no good. What they want is to alienate you from us, so that you may have zeal for them. 18 It is fine to be zealous, provided the purpose is good, and to be so always, not just when I am with you. 19 My dear children, for whom I am again in the pains of childbirth until Christ is formed in you, 20 how I wish I could be with you now and change my tone, because I am perplexed about you! (NIV)
Following Longenecker I see this passage as the start of a new section, the request section. Now that Paul has built the Scriptural and experiential foundation of his appeal he now goes ahead and makes it. The appeal starts with a call for the Galatians to become like Paul, meaning, that just as Paul was loyal to the gospel and died to the law for the sake of the Gentile Galatians, they should do the same. They should be loyal to the gospel by not erecting boundaries where none should be. This reminder of how Paul was when he came to them segues into his appeal on the basis of their prior experience together.
When Paul was in Galatia, the Galatians did him no wrong. They received him with joy, as one who spoke the very words of God, as a divine messenger, and this is amazing because Paul was not impressive in appearance. It's not clear what malady Paul had, but it was fairly noticeable. Usually in the ancient world being a promoter of a religion who had a serious illness would prevent your audience from accepting what you had to say. It showed that you were counterfeit. Not only did the Galatians not reject him, but they were willing to give them their right arm for him. A deep affectionate bond had developed between Paul and the Galatians, which is why Paul was so perplexed by their defection from his gospel. The cause of this was the Teachers.
The Teachers had gone into Galatia and undermined Paul's gospel by telling the Galatians that they had to become Jews to be full members of God's people. Thus they excluded the Galatians from the people of God. Paul goes on the offensive here, stating that the motives of the Teachers weren't pure, they excluded the Galatians so that the Galatians might pursue them. The Teachers wanted a following and swept in upon the vulnerable Galatians. The Galatians thought that the Teachers were helping them, but Paul exposes their true motives.
Paul continues that he wasn't saying this motivated by jealousy, rather it is out of deep concern for the Galatians. Paul cares for them deeply, like a mother for her children. Paul had gone through much labor and anguish to see the Galatians come to know Christ. Now he had to go through it again, but this time from afar. Paul would have preferred not to have to deal with this from a distance, but he had to and so he had to be a bit on the harsh side. On top of attempting to drive a wedge between the Galatians and the Teachers, Paul also was trying to appeal emotionally to the sense of solidarity that the Galatians and Paul once had.------------
 Here I disagree with the NIV's addition of 'from us' to 'What they want is to alienate you.' 'From us' is not part of the Greek text and is an unnecessary addition. The NRSV is preferable at this point, 'They make much of you, but for no good purpose; they want to exclude you, so that you may make much of them.'