Am I a dick for not switching days off with my female coworker?

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no, it's not your responsibility to work for her just because she didn't have the foresight to ask off for her friends birthday.

She fucked up and she can't go, time to sack up and get over it. It's not your problem and you really shouldn't even be wasting your time thinking about this.
"People incapable of guilt usually do have a good time"
-Detective Rust Cohle