Why will no one need to be taught God's Word under the new covenant?

Under the new covenant, no one will need to be taught God's Word because every Israelite will have the heart of God within them. They will be an obedient people of faith and believing, cleansed from all iniquity, rather than depending on external instruction in the law’s commands.

Les teaches that Jeremiah 31 describes the new covenant God will make with the house of Israel, and it will not be like the old covenant of law. In that coming day, no one will have to be taught the Word of God, and no one will have to be told what the law commands. Instead, every Israelite will have the heart of God within them. They will be an obedient people, a people of faith and believing, cleansed from all their iniquity, and they will prosper materially. This fits Israel’s Old Testament economy, where obedience brought God’s material blessing.

Jeremiah 31:31

Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:

Under the new covenant, will anyone need to be taught God's Word or the law?

No. Under the new covenant, no one will need to be taught the Word of God, nor will anyone need to be told what the law commands. Every Israelite will have God's heart within them, being an obedient people of faith and believing, cleansed from all their iniquity and materially prosperous.