I like what you're trying to say, the message is clear. But I think you could have made your diologue a bit more clear.

Here is what I think you could do with it;

"Hello," he answered (answered? maybe said and Areina answered back. possibly started.) quietly.

"Hi," Areina said, "I'm at your school can you meet me at the back of it?" (is this a phone call? and you might want to put in a comma in between school and can.)

"Sure I'll be right there," he answered, a few minutes later he came out to the back of one of the buildings. He hugged her and then got out some food and started to eat, "do you want some?" He asked.(the comma after eat needs to be a period. same with after answered, and you could take out the "then" in between and and got.)

"No I'm not really hungry, I haven't been for a few days," Areina answered solemly. (comma after no, and maybe an "and" in between hungry nd I)

"I see how come?" the boy asked her. (comma or period after see. Make "the" capitol)

"I think you of all people would know," she said bitterly.

"Oh right because of what I told you," He sighed, "you really should just get over me I'm no good for you." ("He" uncapitolized. period after sighed. comma after me)

Areina-chan felt like crying as he said those words but she held back the tears. "How would you know you wouldn't even try? I still don't understand why we can't try." (comma after words. question mark after know, exclimation point after try)

He hugged her as she finished, she was shocked, "get off me," she said bitterly, trying to push him away. (I'll hust redo this completely: He hugged her as she finished speaking, which surprised her. "Get off me," she said bitterly as she tried to push him away.)

"No," was all he said as she struggled to get free. (take out "was all")

When she finally did she was on the verge of tears. "I don't believe you," she snapped, "I'm leaving and I'm never coming back." (when he finally did. the boy is letting go.)

"Fine," the boy said quietly. (this is good.)

Areina stormed away putting her arms around her hugging them to her body tightly. She took one last look at him before leaving the school. (her to herself, and a comma after that)

Overall though, it was a beautiful story, and illistrates an important message. These are believable characters.