I wonder how many times in the History of the Church a resignation such as this took place? Also, why was a reconciliation between him and Pope Paul VI needed?
Paul VI was a very disobedient bishop when he was secretary to Pius XII. He opened up channels of communication with Metropolitan Nikodim against Pius XII's wishes. Pius XII threw him out and denied him a cardinals hat. John XXIII gave him the Cardinal's hat. He was intellectual and political but not interested much in theology as far as Popes go. He was superior to both John XXIII and JPII but well below Pius X, XI , XII. He set the Church on an unprecedented path that had never before been done. He had a rite of Mass drawn up by a committee with Protestant input and no Apostolic roots. (Every other rite in the Church went back to at Least the 1400s and had a root with one of the Apostles. The Novus Ordo has no such connection.
He also allowed Bugnini to attack every other form of every other Sacrament. Paul VI stated in 1972 that "somehow" (incredibly) the smoke of Satan had entered the Church. Then he did nothing about it. Archbishop LeFebvre simply stayed exactly where he was when he was ordained and trained. He refused to aid in the destruction of the Church. As has been pointed out by others, what Pius XII lauded LeFebvre for, he was condemned by those in love with the spirit of Vatican II.