It is his love for Christ that appeals to a master on behalf of his slave. It is here that we find two men converted by Paul's preaching compelled to face their relationship with each other. He is very dear to me but even dearer to you, both as a man and as a brother in the Lord. When slaves become brothers relationships change for the better. Paul has just planted the dynamite and ignited the fuse to destroy the oppressive order of slavery.
Coercion is out of harmony, even contradictory to the spirit of the gospel.
Paul walks a tight wire but he retains his integrity. Coercion does not validate, but violates the gospel. I no longer call you servants, because a servant does not know his master's business. Instead, I have called you friends, for everything that I learned from my Father I have made known to you. Then the Father will give you whatever you ask in my name.