So Superman is kind of legendary at this point. All the boys back home wanted to be Superman (except for Wally he always wanted to be the Flash but he is an outlier and should not be counted). Superman's a living legend not because he's powerful and seemingly invincible, but because he always does what's right and he's always kind. To the people who deserve it, anyway.
Even if Superman back home was something of a jerk (and even if Wally is biased on that because he's got Superboy's back) he's nothing like the one here. I've been over all this already, Superman being a lot nicer here, treating Wally (for the most part) like part of the team instead of just some kid, blah blah, etc.
AS FOR WHAT'S DIFFERENT. Wally is getting a lot more comfortable with the idea of being friends with these people (read: the League) instead of just some kid trying to prove himself. For all the tantrums he threw and all the whining he did, he treated himself as a kid just as much as any of the adults did, if not more. He had convinced himself of their infallibility when it wasn't actually there, and he'd shoved them all up onto pedestals they didn't ask for and judged them for it if they fell. Getting shouted down by Power Girl and then going home and coming back after helping to put the League back home right again had done an awful lot to teach him about actual equality, and now he's ready to UNLEASH THAT UNDERSTANDING ON UNSUSPECTING ADULTS.
As a result Wally's trying to get to know people better as people. That means teasing people, seeing how they react and getting to know them personally. Superman is chief among them, because a) he really likes Big Blue and b) Clark handles his teasing with aplomb. Superman's kind of funny and even if he's a worrywart (AND A TOTAL SHOWOFF!!!) he's kind of fun to be around. Wally's pretty sure he'll never be able to pal around with Clark like he does with Robin or Jaime, but he can definitely get that big brotherly vibe and work with that.
TL;CR WALLY WANTS TO GET TO KNOW CLARK AS A PERSON AND WORK WITH HIM AS A COHESIVE UNIT OF FRIENDS
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So Superman is kind of legendary at this point. All the boys back home wanted to be Superman (except for Wally he always wanted to be the Flash but he is an outlier and should not be counted). Superman's a living legend not because he's powerful and seemingly invincible, but because he always does what's right and he's always kind. To the people who deserve it, anyway.
Even if Superman back home was something of a jerk (and even if Wally is biased on that because he's got Superboy's back) he's nothing like the one here. I've been over all this already, Superman being a lot nicer here, treating Wally (for the most part) like part of the team instead of just some kid, blah blah, etc.
AS FOR WHAT'S DIFFERENT. Wally is getting a lot more comfortable with the idea of being friends with these people (read: the League) instead of just some kid trying to prove himself. For all the tantrums he threw and all the whining he did, he treated himself as a kid just as much as any of the adults did, if not more. He had convinced himself of their infallibility when it wasn't actually there, and he'd shoved them all up onto pedestals they didn't ask for and judged them for it if they fell. Getting shouted down by Power Girl and then going home and coming back after helping to put the League back home right again had done an awful lot to teach him about actual equality, and now he's ready to UNLEASH THAT UNDERSTANDING ON UNSUSPECTING ADULTS.
As a result Wally's trying to get to know people better as people. That means teasing people, seeing how they react and getting to know them personally. Superman is chief among them, because a) he really likes Big Blue and b) Clark handles his teasing with aplomb. Superman's kind of funny and even if he's a worrywart (AND A TOTAL SHOWOFF!!!) he's kind of fun to be around. Wally's pretty sure he'll never be able to pal around with Clark like he does with Robin or Jaime, but he can definitely get that big brotherly vibe and work with that.
TL;CR WALLY WANTS TO GET TO KNOW CLARK AS A PERSON AND WORK WITH HIM AS A COHESIVE UNIT OF FRIENDS