This is not a story where I converted someone, but more of why I started on this path myself.
It was one day after almost a 20hr drive all the way from Italy to the Netherlands. This was after a 3 week holiday. So we (me and my two cousins) arrived all exhausted at my cousin's house. My cousin has a Pioneer receiver in his room with two full-size speakers. He decided to put on Pink Floyd - The Wall for me. I had never heard Pink Floyd before, so I really didn't know what to expect. I sat there on his couch and when the music started playing I slowly but surely got sucked in more deeply. I just found it amazing to hear Pink Floyd play and it just kept getting better and better. I never knew guitars could sound so beautiful. And then when Comfortably Numb started my skin really started to crawl from that absolutely amazing and gorgeous guitar solo by David Gilmour. And it sounded great on his setup.
Now I know it wasn't on a headphone, but hearing that music made me realize that it's time to start investing in better quality audio gear because I want to hear more of those guitars. And I haven't looked back since. So it started with getting a pair of Shure SE100 (or 110, don't remember) IEMs and a world opened up for me (before then it was always the cheap crappy earbuds). I never knew music could sound so beautiful, that there was so much detail, so much nuance. And that was just with the SE100. After that I upgraded to the Shure SE530 IEMs (this was 4 years ago). That really blew me away. All that detail, especially in the mids. Guitars really sprang to life and currently I still think it's one of the best musical instruments out there when properly utilized. And I still enjoy those SE530s everyday. And just today I received my Fiio E12 amp and am currently looking around for a pair of over-ear headphones.
I remember I once let a friend of mine listen to the SE530 and all he said was 'where's the bass?' and all I could do was raise my eyebrows and sigh...