When and how did you, if at all, realize vinyl is better?

Back in the 60's. When I bought my first LP.
I like the convenience of CDs and I listen to them pretty often. Some are even recorded well.
But, when I drop the stylus down, into the groove...magic!
 My neighbors, my friends, find it remarkable when we compare digital to analog. Soundstage, tonal balance, bloom is much more precise (on my system).
 Unfortunately, I find that most reissue LPs are poorly remixed. The recording engineers seem to think that they are improving the original LP by changing the sound- more bass, more vocals, more horns, etc. And they usually screw it up. Luckily, I still have my LP collection and managed to have kept them in good condition.
 

I agree that you can get respectable sound on the cheap with digital. About a year ago I put digital back into my system to listen to the hundreds of cd's I bought during the cd craze (& yes I started on the cd addiction before the high end addiction). I bought an older pioneer elite player & a Parasound dac. It sounds a whole lot better than I remember digital sounding like. In fact when my mood allows & with the right cd, it sounds awesome. That said, it still doesn't hold a candle to the analog portion of the system. But since I've got 5x that into the analog portion, not to mention a whole lot more work (I made the table myself), it shouldn't.  

I had an analog rig exclusively until 1994 when I finally bought an inexpensive Nad 502 which sounded better than the 3 previous more expensive cd players I'd brought home to demo and then promptly returned.
Records just sounded much better.  I had a Kenwood KD-500 w/ Grace 707 arm and Supex SD-900 E+ and it always sounded good compared to any CD I had listened to at the time.  

After the motor on my Kenwood started to not be able to keep the speed consistent, I bought a used Maplenoll Ariadne that took about 6 months to get right--many new parts.  Then, it was a beautiful sounding table/arm.

I kept the Nad for about 14 years, then bought my first NICE cd player--the Modwright Sony 9000.  It was night and day difference and suddenly, some cds sounded better than the records at times.

Fast forward to now, and I have a Modwright Sony 5400 Signature Truth with all the upgrades and it sounds absolutely stunning on some well recorded cds.  Yesterday changed things again.  Since getting a TRL DUDE preamp, I've been looking for a phono preamp that would sound as good as the DUDE.  I went  through a couple with each getting better sounding.  I now have a Whest 3.0 RDT SE phono and it is my idea of sonic perfection, or as close as I'm going to need.  I have a Super Lenco rebuild with most of JTN's upgrades, Trans-Fi Terminator arm, and Benz Micro Ruby 3 w/ myrtlewood body.  Once I finally got the loading right on the Whest, the sound was considerably better than any analog setup I've ever had.  Now, there are a few cds in the same league with the records, but most of the music is a big win for vinyl.  Every single record I've listened to since yesterday has sounded much better than they did with a very good phono preamp I had prior.  Vinyl again rules!!

When? In 1960 when Canada Post shattered on delivery by throwing the package on the doorstep all my childhood post war England original priceless Miller shellac 78s. I thought--all the the way from the UK, and destroyed by a postal worker in the last 2 feet. If they were vinyl that would not have happened. That is when I knew vinyl was better. 57 years ago. The more things change, the more they don’t.

1986. The first time I ever heard a CD player coincidental with my first VPI table. No contest.