Single Status Update
Headcanon: Pre-present Era Shadow may act aloof and "cool", but in reality doesn't get why others see him as what popular media portrays him as (edgy badass edgelord/Furry Batman).
All of the times he crosses his arms and acts aloof and cool in social situations is in reality him just deciding to keep quiet until he can get more information on what's going on and then figure out something from there.
He's intelligent enough due to his time with Gerald to at least pick up on things, but his isolation aboard the ARK, being about 50 years out of date compared to everyone else (though he learns quickly), his only friend at the time being a sheltered ill girl, and his own recent friends being a sassy frank secret agent with a penchant for being at times a tease, and a really maniacal, extremely single-minded and battle happy robot, means that in reality he doesn't know how to deal with a lot of people.
As such, he finds it utterly baffling as to why people (especially kids) find him cool, he finds fangirls weird and doesn't really get or care why people want to act like he's more badass or edgy than what he actually intends to do. Rouge finds the sheer disconnect between the popular perception of him versus the actual person incredibly amusing, and she enjoys being secretly smug about having this little detail privy to herself since it's something she can hold over others, even if only privately.
His time with Maria and Rouge also means that he actually has a lot of hobbies or interests that are considered girly or feminine, but he doesn't really care if they're considered that due to his isolation aboard the ARK, and a general lack of care of the opinions of others outside of those he cares about.
He's like an inverse of Knuckles, who's basically similar in many ways, but who has a tendency to become agitated in situations he doesn't fully comprehend, thus giving him the reputation of being a hothead at best, and a fool who tends to stick his foot in his mouth at worst.
Recently going back and watching the old astroboy anime, I've always thought they looked at atlas the robot and thought about the idea of making shadow like him. He too had a female companion he cared about and he also hated humans at first. Look up those episodes and you might find what I'm talking about.