The Edge assisted Bono in writing the lyrics and felt they were actually about Bono's emotionally-reserved father, Bob Hewson, who was dying of cancer at the time. The outing went quickly awry when the kite crashed and Eve asked if they could go home and play with their Tamagotchis. The lyrics were inspired by a kite-flying outing on Killiney Hill overlooking Dublin Bay that Bono attempted with his daughters Jordan and Eve. According to him, the addition of the solo "really made that part of the song come alive". As a result, they edited in an additional section of the song and the Edge played a guitar solo on his 1964 Gretsch Country Gentleman, which he plugged into an Ampeg Scrambler distortion pedal and a Vox AC30 amplifier. Bassist Adam Clayton called it a "memorable moment", saying, "I don't think we had heard that voice for a long time." With the song near completion, the band was not entirely satisfied and decided it "needed a twist". After hitting a high note when singing the line "I'm a man, I'm not a child", the others in the studio were taken aback. During this process, lead singer Bono said his "voice returned" after several years of him suffering vocal difficulties. After hearing the loop, the others quickly improvised the entirety of the song.
One of these was a loop of a string section that inspired "Kite". Guitarist the Edge said that these group sessions did not produce many great ideas, resulting in him bringing in his own individual musical ideas for them to work on. With Eno on keyboards and Lanois on rhythm guitar and percussion, the six of them composed songs during jam sessions. For three weeks in late 1998, U2 worked at Hanover Quay Studios with producers Brian Eno and Daniel Lanois in hopes of quickly developing new material for a studio album.