I'm pretty much the epitome of this. I don't get attached to every single Pokemon I catch (not since Blue and Red anyway), but if I use it for anything - breeding, false swiping, Cute Charm or Synchronizing to find a certain Pokemon, whatever - it gets a nickname. Depending on how I feel when I get around to transferring things from a game about to be wiped, the vast majority of nicknamed Pokemon get transferred. This can get ridiculous.
Most Pokemon I can leave behind as long as I haven't used them for anything, but certain ones I just like too much. Most of the starters for instance. But most of all, Eevee and any evolutions thereof. I decided to reset my Diamond version recently because I didn't like the name I'd picked for my character. I had about 5 boxes of Eevees. I nicknamed them all and traded them to my Pearl version.
However, my Pearl version is the one I routinely reset. Which means I need to transfer everything I sent to Pearl, back to Diamond. Once all my Eevees are on Diamond, they're going to Pokemon Ranch...
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A bit of psychoanalysis: As a child, most of my friends were toys. That is to wit, most of my friends were imaginary. This has profoundly impacted my attitude towards video games. Some people play characters in games as if they were an avatar of themselves; my cousin doesn't generally play characters that are female or black, because he's a white male. I'm not like this. I regularly roll female characters (despite being male), because I don't consider them an extension of myself. I view them more like imaginary friends. They're separate entities that I guide and take care of.
I see Pokemon the same way. I take care of them. I generally reset my DS any time one of my Pokemon faints, because I know I can do better. Any battle where even one of my Pokemon faints is a battle lost. The only exception is my first fight with the Elite Four on a given game, because I'm typically under leveled against them...