Why did Paul call Peter out in Galatians and what does "obey the truth" mean?

Galatians 2:11-14:

“When Peter came to Antioch, I told him face to face that he was wrong. 12 He used to eat with Gentile followers of the Lord, until James sent some Jewish followers. Peter was afraid of the Jews and soon stopped eating with Gentiles. 13 He and the other Jews hid their true feelings so well that even Barnabas was fooled. 14 But when I saw that they were not really obeying the truth that is in the good news, I corrected Peter in front of everyone and said: Peter, you are a Jew, but you live like a Gentile. So how can you force Gentiles to live like Jews?”

This account helps us understand what it means to obey the truth as well as what it means to walk contrary to the truth. The law prohibits Jews from dining with Gentiles. Paul called Peter out for not obeying the truth after he (Peter) did some "eye-service" and reverted to the Law of Moses by not eating or associating with Gentiles because some of James' Jewish friends from Judea were in town. Peter's action was contrary to the truth. He didn't obey the truth of the Good News:

“But be doers of the Word [obey the message], and not merely listeners to it, betraying yourselves [into deception by reasoning contrary to the Truth].”

The message of the cross is righteousness by faith through Christ Jesus. Romans 5:9 says of how our loving Heavenly Father sees us in Christ:

“And there is still much more to say of His unfailing love for us! For through the blood of Jesus we have heard the powerful declaration, “You are now righteous in My sight.” And because of the sacrifice of Jesus, you will never experience the wrath of God."

Doing of the Law in order to not perish but have everlasting life or to be anything at all in God's sight after Christ died to make us righteous and perfect in His sight is what it means to be a hearer of the word alone and not a doer.

Some church leaders try to compartmentalize the law into moral law/oral law/ceremonial law and say that we who believe are still subject to some of these compartments of the law. What a horrid antichrist teaching! The law is a whole, just like the tree of the knowledge of good and evil (a picture of the law which gives the same knowledge and which many are eating of in a bid to be godly/be like God - see Romans 7:8-12 The Message.) As it was with eating of the tree which has many parts (bark, leaves, root, etc,) eating of any part of the law (the letter) kills, whether moral, oral, ceremonial or the one with which man privately judges himself in his heart (see Romans 2:12-15.) Whatever it is that man does by his arm of flesh/will-power in a bid to become godly like God, to contribute to his godliness or in order to not perish bit have everlasting life is law-keeping.

Romans 7 also shows us that the law that we who believe are dead to includes the Ten Commandments; Paul used the 10th Commandment (You shall not covet) as an example in this chapter. In Christ, we are not under law but under Grace. We have no righteousness of our own. The Lord Himself is our Righteousness. In Christ, we have salvation from every sins, earthly ill and death in hell.

Paul goes on to say in verses 17–21 of Galatians 2:

17 “But suppose we seek to be made right with God through faith in Christ and then we are found guilty because we have abandoned the law. Would that mean Christ has led us into sin? Absolutely not! 18 Rather, I am a sinner if I rebuild the old system of law I already tore down. 19 For when I tried to keep the law, it condemned me. So I died to the law—I stopped trying to meet all its requirements—so that I might live for God. 20 My old self has been crucified with Christ. It is no longer I who live, but Christ lives in me. So I live in this earthly body by trusting in the Son of God, who loved me and gave Himself for me. 21 I do not treat the grace of God as meaningless. For if keeping the law could make us right with God, then there was no need for Christ to die.”

Interpreting or acting on the belief that being a doer of the word is obeying the Ten Commandments and doing works of the law in order to be anything before God is rebuilding the old system of the law that we who believe in Jesus already tore down. It is treating God's grace as meaningless.

“Law” and “Grace and Truth" are on different sides of the aisle, “For the law was given through Moses, but grace and truth came through Jesus Christ.” John 1:17.

For we who are in Christ, this truth is not “obey the Ten Commandments in order to be righteous.” No one can (Romans 3:20.) This is the sure-fire way to get cut off from Christ:

“For if you are trying to make yourselves right with God by keeping the law, you have been cut off from Christ! You have fallen away from God's grace.” Galatians 5:4.

Peter reverted to the old way of trying to keep the law in order to be seen as righteous before the Jerusalem crew.

Our truth is that in Christ, God sees us as righteous only because of the shed blood of our Saviour Jesus Christ. All who receive God's abundance of Grace and obey the truth (believe and receive His gift of righteousness to us in Christ) GET TO live in triumph over sin and death through Jesus Christ: Romans 5:17-

“For the sin of this one man, Adam, caused death to rule over many. But even greater is God’s wonderful grace and His gift of righteousness, for all who receive it will live in triumph over sin and death through this one Man, Jesus Christ."