An "origins" episode of a TV show or superhero comic shows that a ton of nasty stuff happened to Alice in her life, and that she's very emo about it. She suffers from depression and has attempted suicide in the past.
She's born like this and it alienates the hell out of her (both in-story and in the viewers) due to the fact that she will feature stoic reactions to what should be emotional scenes (violent murders of relatives, heartwarming reunions, etc.) She may even justify it by asking something like "Why should I feel emotions to these scenes when they are so common?"
Her emotions are deliberately suppressed (by magical or medical means) because she's Ax-Crazy with emotions.
She has emotions, deep down, but she cannot process them well around others, and forcibly closes off her heart and mind to even her closest friends, fearing what they'll think if she shows her true self.
Reconstructed: She decides to seek some therapy, but still doesn't turn into a ball of smiles.
Played For Laughs:
Alice is unfazed by the bizarre goings-on around her or causes embarrassing situations for other characters. She walks in on her friends changing to ask what they want to eat, walks across the rickety Rope Bridge without a second thought, and asks the giant monster where the nearest grocery store is.
Played For Drama: Alice really wants to experience emotions, but because she's a Barrier Maiden, she can't risk showing them without potentially causing massive destruction. Characters around her aren't necessarily aware of this fact, and constantly try to cheer her up or otherwise make her emotional.