I'd like to start giving people the option of commenting on shorter Cold Takes pieces (which I don't cross-post here or provide audio for). I'm going to use this post for that: I will generally leave a comment for each piece, and people can leave their comments as replies to that.
I've felt flummoxed for a while about Pet Sounds. I first tried listening to it in high school (after learning of its acclaim) and couldn't make it through. When I listen to it now, over a decade later, I feel I can clearly hear and appreciate the "symphonic" quality of the songs, and the care and craft that went into the production, instrumentation, and compositions. It's not difficult for me to believe that it was a major leap forward and I think it's not too difficult to hear how influential it's been. A song I love, "John Allyn Smith Sails" by Okkervil River is partly an adaptation of "Sloop John B".
Moreover, when I listen to Pet Sounds with 'audiophile brain' the sounds, melodies, and harmonies all sound great. But I just don't enjoy listening to the album. The vocals sound detached and clinical to me. For such an acclaimed and highly-ranked album, I feel it doesn't have many raw emotional hooks.
Compare to others on the top of the lists Holden linked: Marvin Gaye, Nirvana, The Beatles, Joni Mitchell, Dylan. Their songs have some powerful emotional energy that Pet Sounds seems to lack-- and will typically make you feel something, even if it's not your cup of tea. To me, Pet Sounds sounds like the odd one out, so I still feel confused why it's so high on these lists.
Also, I would definitely rank A Love Supreme much closer to the top.