8:10-11 What does it mean here that no man will teach his neighbour or brother?

This is quoted from the Old Testament prophet Jeremiah (CP V8-13 with Jer 31:31-34).

It means that there will be no need for intermediates such as the Old Testament priests and scribes to teach men about God under the new covenant. The Holy Spirit will lead them in all truth (CP Jn 14:25-26; 16:12-15; 1Cor 2:13-16; 1Jn 2:20-21).

The Old Testament priesthood together with the law will be abolished (CP He 7:11-12, 18-22; 10:9-16).

Under the new covenant every believer will become a priest of God (CP 1Pe 2:5, 9).

None of this is teaching that Christians have no further need for teachers. God has set teachers in the church and they will remain there until His purpose for the church in the earth is fulfilled (CP Eph 4:11-15; He 13:7, 17).

It should be noted in closing here that 1Jn 2:20 is not teaching that Christians know everything; that there is nothing left for them to learn, but simply that they know all things necessary to salvation, and they do not need to be taught by those who seek to deceive them (CP V18-27).