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

I've realized that the premise is not necessarily true. I’ve listened to lots of vinyl for decades and now use a CD player as my only source. I believe you can assemble (craft) an audio playback system so CDs will sound just as good or better than vinyl. Each step of the way, while improving (striving for a certain preferred sound) my current system piece by piece, iteratively, its only source was digital. End game: CDs sound terrific on my current system. I think often times people who believe vinyl sounds better are judging based on playback on a system which was not purposely crafted for a digital source.

Rockadanny, I for one would emphatically disagree with that premise!
My system over the past 15 years was changed, upgraded, focused on digital sound including multiple turnover of digital components to try to achieve a less fatiguing presentation of music.

I can only say that my recent focus on vinyl playback has eliminated any ambiguity as to which I prefer. It is as it has always been as the two are different mediums. To me it's not even debatable. Maybe because of my age and growing up in the golden age of audio.  I  believe that the relatively recent  renaissance of vinyl playback is a connection to the emotional aspects of musical playback which is the heart of the matter. It seems many younger listeners, contributing to this renaissance also recognize this as well. What is going on here? Is this a  nostalgia trip or is there something deeper happening? 

To me is is quite clear in the here and now that the main advantage of digital playback, for the most part, is convenience. I have had more than the last 30 years to compare,  no ambiguity on my part, vinyl still reigns supreme in musical engagement. Having said that I completely respect the opinions of those that disagree, whatever floats your boat.

I agree that the premise is a bit funky, even if I prefer analog.  For one thing, "better" depends on what music you're listening to.  If you only listen to contemporary music, I doubt you're better off trying to hear it all in vinyl. No point in adding a layer of distance from the original digital recording. OTOH if you're primarily listening to music recorded before the Reagan administration (ok I admit it) then vinyl makes more sense.  

You will realize vinyl is better if you like snaps, crackles and pops.

In many cases ticks and pops are actually artifacts of the phono section; while the actual tick or pop is on the LP surface, if the phono section is unstable it will exacerbate the tick and make it a lot louder than it really is on the LP. IOW phono preamp design has a huge effect on this and its not a bandwidth thing.

 If you only listen to contemporary music, I doubt you're better off trying to hear it all in vinyl. No point in adding a layer of distance from the original digital recording.

The assumption here is that all modern music is digital and all mastered the same. Its not.

When mastering an LP from a digital source, the LP usually does not employ as much compression since there is no expectation that the LP will be played in a car. Further, the mastering house if often working with the master file that has far less processing applied than the file intended for digital media. So even though using a digital source file it can still sound better.

But analog tape is seeing a comeback too, and pro analog multitrack machines are going for a lot more now than just 5 years ago as demand has increased. IOW there are new LPs coming out now that are recorded analog.

Add to that: vinyl of new titles is a lot easier to find these days!

I have had more than the last 30 years to compare, no ambiguity on my part

Same with me. Perhaps I just got lucky with my choice of components.