The bike of "Eugene's Bike" is so kick ass, with fat tires and a triangle flag and a baseball card flicking on the spokes. This is huge for Eugene, who was given the bike as a “Flag Day” gift. It’s the one thing he’s wanted more than “anything else,” more than world peace even! When Arnold knocks over Eugene’s bike into the middle of the street, they are both crushed (as crushed as that perfect red flag-day bike). Arnold feels terrible, but Gerald tells him not to worry about it too much, because this “always happens to the geeky kids”. This statement has some perceived wisdom, and it suggests this: geeks deserve their bad luck. Arnold’s response, though, is not passive agreement. In fact, after dwelling on Eugene’s unlucky past, he shouts, “every dork deserves his day, and I’m going to give it to him!” This is noble empathy, especially noting that Eugene tucks his shirt into his underwear (a nice touch by the animators).
Arnold’s empathy doesn’t stick around, though; it quickly changes into an obsessive need to fix Eugene. He breaks the bike, “I’ll make it up to you”; he puts Eugene in the hospital, “I’ll make it up to you”; Eugene gets mistaken for a tonsillectomy patient, be sure to wear your “fun clothes”, Eugene, because Arnold is going to “make it up to you”! This obsession feels less empathetic and more insecure in their friendship. This is basic attachment theory - Arnold’s anxiety reads preoccupied and untrusting. At the conclusion of the episode, after planned fun day, Eugene is throwing up over the edge of a local bridge, and Arnold sits sadly and sorry. “I guess this wasn’t such a good day, after all,” he sighs. There’s an assumption that their friendship is intrinsically connected to Arnold’s ability to “fix” those he has wronged. This feels a little like a friendship of utility (as if to say, “if time spent together isn’t successful, what’s the point?”).
Eugene sees their friendship differently. Even at Arnold’s first attempt to make things right, he says (of his fixed bike), “you didn’t have to do this, Arnold!” He says this phrase over and over, as Arnold tries (and fails) to make it better. His joy doesn’t really falter, either. He truly sees Arnold as a friend. When Arnold mourns their fun-day turned not-fun, Eugene smiles and says, “you know, nobody has ever done anything like this for me before.” He sees their flubbed day not as a failure, but as a complete success. Eugene understands that just BEING together is a sign of true friendship. This is unconditional love and true understanding. Arnold gets it, too - Eugene’s arm gets stuck in the bus door, and has forgotten his favorite baseball card, and yet, Arnold’s anxiety is gone. These things just happen, he’ll give Eugene that Spuds McGee baseball card tomorrow. And friendship will live on.