It's not because of fidelity
I'll start by discarding one reason: fidelity. Fidelity is the ability of a system to reproduce a signal with the least amount of change. High fidelity means little to no change is being induced, low fidelity means too many change is being induced. Perfect fidelity means the signal is being reproduced perfectly, without change at all.
Your typical vinyl setup induces a lot of change. From the phase change produced by the RIAA curve, surface noises, low dynamic range (when compared to 16 bit), to inner and outer portions sounding different.
Objectively, judging by measurements, in the context of fidelity, 16 bit 44.1 kHz PCM (also known as CD quality) is by far superior to vinyl. You can read more about it here, here, here, and here.
Now that we established what it isn't about, let's dive into why vinyls can offer a superior musical experience.
It's about the vinyl sound
Vinyl's lack of fidelity (again, in relation to CD quality) is a plus in the ears of many. For those people, these added characteristics ("analog warmth", or whatever you want to call it) are pleasant, so they seek them.
Interestingly, some of the "analog warmth" seekers are also high-fidelity enthusiasts. But the more you move into objective high-fidelity territory the less change (the less "analog warmth") is induced, so the more they invest in equipment the less "analog warmth" they receive.
And also about misconceptions
Not sure why, but the incorrect notion that vinyl has higher fidelity than CD (and other mediums) is widely spread. Many vinyl and audio enthusiasts in general seek vinyl based on that notion. They think they are building a superior system, so getting into vinyl seems like a natural move.
No, the sound in digital is not getting "pixelated". As long as you are working within the Nyquist frequency, the sound is being reproduced perfectly fine. Mathematically, the original and sampled versions are the same.
The DJ scene is in a huge boom. It has never been so easy and affordable. Many of those digital DJs will make the transition to vinyl, which carries a very specific skill set and feel different from playing with CD players or software.
And the vinyl ritual
Vinyls are awesome. They have the waveform engraved, you have to place it in the plate and place the cartridge, select speed, clean everything, that kind of stuff that elevates the listening experience to something more artisan, more involved.
They are big, but slim, so they are great for hanging on walls, or collecting. It's an old technology, so it has this old-school vibe for some, maybe nostalgic to others.
If I had to condense it in a few words: because people like its sound (even if in some cases they are being deceived by their biases and misconceptions) and the artisan-like rituals involved with everything vinyl.