I wouldn't call it an obsession, but I can see the appeal:
#1: Eevee is cute.
#2: It is quite rare in earlier games, often giving only one or two Eevee throughout the whole game. This made Eevee's evolution one of those pokes that identified what you liked and didn't like, and set you apart from other players. it was kind of cool in that respect.
#3: The eevee were quite strong back then, and even today they pack a punch. 3 of those evolutions (Jolteon, Espeon, Vaporeon) are on Smogon's OU list, and for good reason, too.
#4: There is enough of them to make a gimmick team. --- Rest in Peace City of Heroes: April 27, 2004 - November 30, 2012. We will miss you. Cause of death: "Realignment of Company Focus" by NCsoft.
because regardless of which evolution you choose for your eevee it is always a great pokemon. however, jolteon, espeon, vaporeon and even umbreon are among the best to choose depending on your preference for a team.
Vaporeon is just beastly with it's Health and then Sp. Atk
Espeon has amazing Sp. Atk and then Speed
Jolteon is speedy as all hell and has great Sp. Atk to support it
Umbreon has a knack for walling almost every attack coming its way
Leafeon tries being Physically defensive while boasting physical attack too, yet it's a grass type
Glaceon is a weaker form of Vaporeon, but favors Sp. Def over health
And Flareon takes the biscuit with tremendous Phys. Atk, and great Sp. Def, yet most of it's moves for it's typing are special based at best with fire fang and flame wheel being an exception and it refuses tp learn falre blitz which has made many players rage quite a bit. Gen 1-3 it really did stink as an eeveelution and only got slightly better over time