Vinyl made a comeback for numerous reasons.
1. The argument that CDs only reproduce the human hearing range, 20-20,000Hz anything else is ditched. Logical as if you can't hear the sound why recreate it on the CD? Purists would argue the sounds you can't hear affect those you can. Music should have been recorded in an analogue manner and reproduced the same.
2. CDs sample sound at specific points on an analogue wave form. Purists will say that this isn't enough and is turning a downhill slope of sound into something like a flight of stairs.
3. Vinyl sounds "warmer." CD etc sounds too good, too pure, too clean. In a similar way people like cinema showing film at 24 frames a second and not more often even though it should be smoother. (Known as the soap opera effect).
4. If you go to the trouble of putting on a record you might actually take the trouble to listen to it. I mean "really" listen to it.
5. A money - satisfaction loop. A cheap CD player does the same job as a good one. A decent CD player tends to have a better DAC, better construction, smoother operation, but essentially a cheap CD player and a good one can both read the "zero's and one's" from a disk just fine. With vinyl the more you spend on a turntable the better sound you get. People like this cost - reward situation. Note, chances are the original source was recorded digitally and is then sent to both vinyl and CDs, a CD might actually give the best rendition.
6. Some other things, vinyl could only go so "loud." Cut too deep into a record and you could cut through it, CDs didn't have that issue meaning they could be mixed louder. See "the loudness war."
7. Vinyl also set how a record should be arranged. What tracks are best where etc. Techmoan explains why this record was mixed to play from the inside groove to the outside one.