Recent thread asking some of the same questions. It’s not that Harrison couldn’t play a guitar solo, but he didn’t like the way his takes sounded and thought Clapton would do it better. The Beatles did not have a lot of guest plays (as opposed to session musicians) on their albums, which is one reason Clapton says he initially said he didn’t want to play on the song.
Back then it was unusual for pop records to list session or guest musicians, which is why there’s so much misinformation flying around about which hit songs Jimmy Page played guitar on and such. I believe that tabla player Anil Bhagwat was credited on George Harrison’s “Love You To”, but other than that, I think the first guest player to be fully credited on a Beatles record (i.e., mentioned by name on the label or cover) was Billy Preston (the “Let It Be” sessions). (Hmmm… now I’m thinking maybe George Martin and Mal Evans might have gotten credits on Rubber Soul, but that was about it.)
If you want some dirt along with musical info, Clapton and Harrison were friends. And then Clapton and Harrison’s wife (Patti Boyd, George met her on the set of “Hard Day’s Night”) began a very lengthy affair. Boyd and Harrison eventually divorced, and Boyd married Clapton.
Although she wanted children, Patti Boyd had none with either Harrison or Clapton.
George eventually remarried, and had a son, Dhani.
~VOW
Clapton’s (then-) unrequited passion for Boyd was the inspiration for Layla and Other Assorted Love Songs. Like you said, her relationship with Clapton didn’t last, but Clapton and Harrison remained friends.
Another reason George brough Eric on is that John and Paul were giving him a hard time about recording the song. They didn’t feel it was “Beatle worthy.” So George brought Eric in one day and basically said "Eric’s here to perform guitar on ‘While My Guitar Gently Weeps,’ basically daring John and Paul to say, “We’re not recording it.” Or so I’ve read.
Others have already answered this. But a side note: Eric didn’t feel his solo sounded “Beatle-y” enough, so they distorted it to give it that wobbly sound.
This was, I believe, the first and only time a non-Beatle played an instrument normally played by a Beatle (aside from a session musician playing for Ringo on their earliest recording) on one of their recordings. Other musicians came in and played sitars, keyboards, strings, woodwinds, etc. And Beatles switched things up with Paul hopping on drums, George picking up the bass, etc. But this was the only time a non-Beatle played guitar on one of their recordings.
Patti and George also remained friends. The divorce was amicable and calm.
After (or maybe at?) the Patti-Eric wedding, George said that he and Eric were “Husbands-In-Law.”
(My now standard disclaimer applies: That’s IF my memory is correct.)
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Harrison was co-author and played rhythm guitar on Badge from “Goodbye Cream,” but was credited as L’Angelo Misterioso due to contract issues. So there was a lot of cross appearances.