
Hmmm, normality. What does it mean? In all honesty, I really don't like the word because I don't think it exists. Nonetheless, we all still say sometime like, "I wish I was just normal..." And exasperated I ask, "What is normal? Does it really exist?"
I think that when people talk about normality, they're expressing that they want to be something that they're not. Or they want to be going through the opposite of what they're currently (negatively usually) experiencing.
The definition of normal is: 1. "Conforming with, adhering to, or constituting a norm, standard, pattern, level, or type; typical." So it's going with the grain, instead of against it. I never would want to be complacent (a word I often use for normality).
I think you sum it up nicely, and I like how you say "Maybe what you wanted in the first place was not to blend in, but to simply be connected."