Complex sentence: The song was initially written by David Crosby but he was fired from The Byrds shortly after he had introduced the song to the rest of the band, although work had already begun on the song's instrumental backing track by the time of Crosby's departure.
Split into simpler sentences: The song was initially written by David Crosby but he was fired from The Byrds shortly after he had introduced the song to the rest of the band. However, work had already begun on the song's instrumental backing track by the time of Crosby's departure.