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In series one of Supergirl the TV series, why was Supergirl unable to breathe in space?

In the Supergirl episode "Better Angels" we have the following exchange between Kara (Supergirl) and her sister:

Alex: Once you're in space, there's no atmosphere. There's no gravity. You wouldn't be able to generate thrust, you wouldn't be able to breathe, you wouldn't be able to get back.

Kara: There is no other way.

My question is, why was Supergirl unable to breathe in space?