Despite his own background, Paul now regards his achievements and gifts as of little value. Again, from A&W, "he is convinced that through Christ, God is fulfilling God's promises by welcoming the Gentiles."
In their People's New Testament Commentary, Eugene Boring and Fred Craddock relate this passage to 2:6-11 that describes Christ as giving up all claim to equality with God in exchange for obedient service:
Paul tells his own story here for the same reason. Giving ourselves up to God is total trust, having no claims, seeking no advantage, but in service to one another leaving our status before God entirely in God's hands.