"A Man and a Woman" emerged after U2's engineer was trying a mix of something the band had recorded. Lead singer Bono liked it and soon started to play the bass guitar and singing. The acoustic guitar that The Edge is playing in the song was taken from another completely different song, they chopped it up and connected together with the new one. It was inspiring to Bono to keep working on that. Bono cites Thin Lizzy founding member Phil Lynott as the influence for the style in which he sings the song.
Bono, who has been interested in the distance that lies between men and women, wrote this song about rediscovering a kind of flirtatious and romantic love. The Edge classes "A Man and a Woman" as the wild card on How To Dismantle An Atomic Bomb.