In v12 Paul pleads with the Galatians to “become as I am”. I’m not really sure in what way Paul means for the Galatians to become as he is. He could mean he wants them to enjoy their freedom from slavery as much as he does, or he could mean he wants them to stand up for the gospel of grace even if it means they’re going to suffer for it, e.g. persecution from the Judaisers. i.e. unlike Peter in ch2 who gave in to fear of the circumcision party and so went along with their hypocrisy, Paul wants the Galatians to stick to the gospel in the face of persecution like he does – in chapter 5 v11 he says “if I… still preach circumcision, why am I still being persecuted? In that case, the offence of the cross has been removed.” If we preach the gospel, we have to expect to face opposition, but Paul’s not talking about opposition from the secular world, he’s talking about opposition from religious legalists, who go by the name of Christian, but their “Christianity” requires people to do works rather than trust in grace alone.
“I also have become as you are” – The Galatians saw Paul practice what he preached in 1 Corinthians 9v19-23 – i.e. rather than Paul making the Galatians follow his traditions in order to become Christians, Paul became like them (as far as possible without disobeying God). He’d made a point of becoming like the Galatians, to show that it was Christ that made them Christians, rather than following certain rules, so it was frustrating to see other teachers coming in and persuading them otherwise, but…
“You did me no wrong.” – Paul clarifies that he’s not saying all this because he’s taken personal offence at the Galatians turning away from what he taught them. His passionate language is due to his passion for the gospel. He’s not trying to emotionally blackmail them into following him instead of these false teachers.
I think sometimes it can be tempting to try to manipulate people to get our own way. “I think we should do things this way in church, and since you’re a Christian you’re obligated to love me, so you should let me have my way.” We probably wouldn’t make it that obvious, probably don’t even realise we’re doing it, or maybe we don’t even actually act on it, but just hold a grudge against someone because they’ve got their way rather than us getting our way. Paul is not concerned about personal grievances, but about the gospel; he sacrificed his own traditions and preferences for the sake of the gospel.