Rachel tells people that she cries cutting onions because onions have layers like she does, because they look like she'd look if everyone could see the way she pushes her feelings out. She likes thinking of herself surrounded by nested auras, one for every song she's ever emoted her way through.
Rachel tells people that she cries cutting onions because she and Jesse had eaten onion rings together, because he'd acted out an elaborate fake proposal with an onion ring. She says that Finn was her first love, but Jesse was her first beau, someone more sophisticated in his courtship and in his betrayal.
Rachel tells people that she cries cutting onions because a star keeps her emotions close to the surface, because her tears are another tool of her craft always at the ready. She wants them to know that she's vulnerable on purpose, using the depths of her self to rise to new heights.
Rachel cries cutting onions because they make her eyes burn the same way they make everyone's eyes burn, because she's never mastered cutting them in a special way or under water or any other trick. She hates that it's so mundane, but there it is: Rachel Berry is, sometimes, just like everyone else.