1 Timothy 1:6-7 - They do not understand the law

6 Some have deviated from these and turned aside to fruitless discussion.
7 They want to be teachers of the law, although they don’t understand what they are saying or what they are insisting on.

vs. 6 - "deviated from these" - Some have moved away from sincere faith, good conscience, pureness of heart, (See: verse 1:5 from previous notes) and the doctrines Paul has been teaching. Instead of living for Christ they become a debating society - arguing about - whatever. "Is smoking worse than dancing?" "Is playing cards worse than going to movies?" “Should we have loud music in our worship service?” “Should believers drink alcoholic beverages?” These all seem relevant and important at the time. This is not bashing clean, moral living. There is nothing at all wrong living a pure life. Arguing about rules for living is no more profitable than is arguing about what is ‘work’ on Sabbath.

vs. 7 - "They want to be teachers" - All the discussion and arguments are to gather information, to marshal their rebuttals so as to convince others they are correct. The arguments are not always to bring people to God, or to faith, and to help in discipleship.
However, and this is BIG: they don't know what they are talking about. Like some of our politicians, they talk even though they are ignorant. "Having nothing to say, they say it anyway."
Is Paul referring to the Jews, to Pharisees or Sadducees? I am not sure. (Many of the early churches had converted Jews in the majority of their congregations.) But he is saying there are 'teachers' who do not understand why the Law was given, its purpose. If they are teaching the Law as a means of salvation or growing in maturity in the faith - they do not know what they are ill informed. If the festivals and holy days and sacrifices are necessary for salvation - they don't understand.

The leaders in Israel did not understand the Scriptures or the power of God. These were best and the brightest of the day! Jesus called them out. See Matt. 22:29 They didn't know! How could they not know? I am not picking on the Jews, because Christians today can suffer from the same malady. In Luke (Also: Matt. 17:14-18; Mark 9:14-27), a father appeals to Jesus to rid his son of a demon (probably epileptic-type seizures), because the disciples failed. See: Luke 9:37-43 Jesus expresses frustration (at least that's the way it appears) saying, "You unbelieving and perverse generation..." (This is also found in Matt. 17:17). He is not talking to the father. The father had just appealed to Jesus when other attempts failed. Jesus is addressing the disciples and the crowd of people who sought Him out as he came down from the mountain after the Transfiguration. The disciples only had an inkling of what Jesus was doing, or what He would accomplish that fateful Passover day and three days later.

Why did Jesus chastise the Jewish leaders? They had drifted away from God. (A recurring theme in scripture - for example read the book of Judges.) In another confrontation, Jesus was asked to heal a paralytic. He told the supplicant his sins were forgiven. (Mark 2:2-12) The religious leaders were upset. How could he forgive sins? Only God can forgive sins, right? Jesus asks them which is easier: forgiving sins or healing a cripple? Don't both require God's power, God's grace, and God working through Jesus? They have no answer. So Jesus heals the man. They are astounded! That’s what I mean in saying the Jews had drifted. How could they be so far away?

In 1 Tim. 1:7-8 Paul is warning that those who want to add The Law to the Gospel are leading the church stray. They don't understand what they believe. The Jews had drifted from the purpose for the Law, and the festivals, and the holy days, and sacrifices - they had lost their way. The Law, including the dietary rules and instructions to worship the Lord were given to set the Jews apart from the heathen, Gentile nations that would surround them in the promised land. If they followed these rules they would be totally different from all the nations, tribes and cultures around them. This difference was to be a beacon, a light to those around them.

Why be a light? To draw people to God so they could experience His grace, His love. Instead, their way of life became a shield, a bulwark against other cultures. The Jews became so insular that it became a 'sin' to touch a non-Jew - just touching a Gentile caused the Jew to be unclean - just like touching a leper! This was a perversion of the Law. Instead of drawing people to God, the Jew's behavior drove them away. In Jesus's time, the Greeks hated the Jews because of their belligerence. The Romans despised and hated the Jews for the same reasons. The Romans finally had enough, so 30 or 40 years later flattened Jerusalem. Rome crushed the Jews as perhaps they had never been crushed before (maybe the Assyrians did a similar job on the Northern Kingdom. Babylon did something similar in Daniel’s time.). There was no sign of God's grace and love here! God tells the Jews they are honoring Him with their lips, but not with their heart or actions. The prophets warned the Jews their hearts were hard, (Ezek. 11:19) not softened by God's grace. They followed their wicked hearts (Jer. 11:8); their idolatry controls their hearts (Hos. 5:4). See also: Ezek. 16:30, 33:31. In Malachi, God recounts in conversational style how the Jews have dishonored Him. The Jews were no longer a tower of light drawing people to God.

That is the danger we face as believers. That the Jews were to be different from nations around them was to remind the Jews it is was God that saved them, not themselves. The Jews were to be able to bring others to salvation. We are to be different from the non-believers all around us. How will people know we are His people? By our love. The greatest commandments: Love God, and love your neighbor. (Matt. 22:37-39; Mark 12:30-33) Jesus appeals to God the Father in prayer that we will love as He loves us, as the Father loves Jesus. (John 15:12,17; 17:26) This message of love, for each other, for non-believers is repeated through all of the letters of Paul, or John, or Peter and others. See Gal. 5:6. People will not be drawn to belief if we hide in our churches, hiding behind stone hearts. We do not need stone castles with moats and drawbridges to hide from the world, to be protected from the world. Hiding will only make us weaker. We need to be in the field of battle. We need to be out there where the people live to show them God's love. How will they come to know Jesus if we don't share Him? No one will want to come Jesus if they look at us and are repulsed. We must not lose our way.

That the Gentiles are to be part of God's kingdom has been known almost from the beginning. Go read God's response to Adam and Eve after the fall, or his Covenant with Abraham. The whole world is to be blessed. Here are a few of the verses: Psa. 22:27, 66:4; Isa. 2:2-5, 9:2, 66:1, 12, 23; Jer. 16:19; Dan. 2:35, 7:13-14; Amos 9:11-12; Zech. 8:20-23; Mal. 1:11. That Gentiles are going to be God's own possession is clearly stated in Hos. 2:23 - “those who are not my people shall be my people“. Our response is, “You are our God!” And in the New Testament, Paul writes in Eph. 3:3-5 and Col. 1:26-27 that Jews and Gentiles shall be co-heirs of the Kingdom of God. However, HOW the Gentiles become co-heirs was a 'mystery' - something revealed to us now, but was hidden from old - See Eph. 2:12-16 "remember that you were at that time separate from Christ, excluded from the commonwealth of Israel, and strangers to the covenant of promise... you who formerly were far off have been brought near..." Also remember that Jesus told his disciples that they would not be able to see His kingdom, as they saw Rome, or the kingdom of David and Solomon. They would not see it because it was within in them - Luke 17:20-21.