Note 1 at Gal. 5:13: Christian liberty is not freedom to sin but freedom from sin. Paul's defense of grace is not a promotion of sin. On the contrary, he is admonishing them to live godly lives. However, the motivation behind our actions has to change. Instead of living holy to be accepted with God, we now live holy because we have been accepted by God and it's our nature to do so. Also, as explained in note 5 at verse 15, page 1082, if we don't walk in love with others, we will be devoured by the strife we sow.

Note 2 at Gal. 5:13: Paul has been promoting freedom from the laws and regulations of the Old Testament law. This is possible because our born-again spirit is changed (see note 9 at 2 Cor. 5:17, p. 1005). In our spirit we are righteous and truly holy (Eph. 4:24) and the Lord relates to us according to who we are in the spirit (Jn. 4:24).

But we aren't only spirit. In this verse, Paul recognizes that there is still a part of us that is susceptible to sin, i.e. the flesh (see note 3 at Rom. 7:18, p. 790). Paul goes on to explain in this chapter (vv. 16-17) that you can't walk in the Spirit and walk in the flesh at the same time. It's one or the other but not both simultaneously. Therefore, if we want to enjoy our liberty which is in our spirit, we must deny the flesh.

Note 3 at Gal. 5:13: How do you deny the flesh as Paul had just instructed (see note 2 at this verse, above)? Paul gives the answer here. The way is to serve others through God's kind of love. Love is unselfish and therefore diametrically opposed to our selfish flesh. Serving others with God's love will always negate the power of the flesh.