The “liberty” we are “called to” (v.13) is our freedom from the condemnation of the law (IICor.3:9), Paul says not to use this liberty as “an occasion to the flesh.” The “flesh” here is the part of you that wants to do the sinful “works of the flesh” (Gal.5:19). So Paul is saying: Don’t use your freedom from the law as an excuse to break the law.
“Serve one another” by love instead (v.13). Paul explains what that means in verse 14, where he says the law of the 10 commandments is fulfilled in the command to love one another. If you love a man, you won’t lie to him or steal from him. The Jews did those things by law because they were a kingdom, and kingdoms must have laws. We do them “by love” because we are a body, the Body of Christ, and members of a body serve the others because they love them. Sinning against them would do them a disservice, not a service.
The Lord said the law was summed up in two words, love God and your neighbor (Mt.22:36-40). But today, God dwells in believers (ICor.6:19,20), not in Solomon’s temple as He did under the law, so in loving your neighbor you’re also loving the God within him. “Neighbor” can mean an intimate, as in the intimate members of a family.
Paul was telling the Galatians this because they’d fallen into biting and devouring one another (Gal.5:15) instead of being willing to serve one another like they used to (4:15). You see, putting yourself under the law as they did always makes you feel “holier than thou” (Isa.65:3-5) and judgmental of others. I.e., “I was in church on the sabbath day (cf.4:10), where were you?” This causes others to envy your supposed holiness (Gal.5:26), which provokes them, as Paul says.
Legalists mean well. If they see you struggling with adultery, they encourage you to cite “Thou shalt not commit adultery” to deal with the temptation. But due to the fallen nature we inherited from Adam, that just makes us want to sin all the more (ICor.15:56). The way to deal with the temptation to sin is to “walk in the Spirit” instead (Gal.5:16).
That has to do with being “led of the Spirit” (Rom.8:14). Matthew says the Lord was led of Him (Mt.4:1) because he presents Him as a king. But Mark says the Spirit drove Him (Mark 1:12,13) because Mark presents Him as a servant. It’s Mark who tells us He didn’t know the day of his coming (Mark 13:26,32) because servants don’t know what their masters are doing (John 15:15). You drive servants to do things by giving them orders and punishing them if they don’t obey. But you can only lead a king to obey you.
Children are also ordered and beaten if they disobey (Pr.22: 15) because they differ nothing from a servant (Gal.4:1). Under the law, God treated the children of Israel as servants, ordering them to do things and spanking them with the “rod” of bad health and bad wealth if they disobeyed. But we’re not under the law (Rom.6:15), so we’re no longer servants, we’re sons (Gal.4:3-7). And you get adult sons to obey you by leading them with instructions and hoping they’ll follow your lead.
And that’s how the Spirit leads us as God’s sons, by instructing us through His Word, and hoping we’ll follow His lead. Paul says if you’ll walk in the Spirit, following His lead, “ye won’t fulfill the lusts of the flesh” (Gal.5:16). It doesn’t say you won’t have them. It says you won’t fulfill them.
Does it always work? No, but it is the only thing that has a chance of working. Walking in the law sure won’t work, for the law only makes sin more sinful (Rom.7:13). It looks like it would help you say no to sin, with all of its “thou shalt not’s. But gasoline is a liquid, so it looks like something that would be good to put out a fire. But as you know, it only makes a fire worse, and the law only makes sin worse. Walk in the Spirit instead by following His lead.