Was anyone else tripped up trying to categorize "The keycard is valid, or the door stays shut."?

This is an exclusive Or yes? So we can't have the keycard be valid with a shut door, it's got to be one or the other. I translated the original statement into:

1. if the keycard is valid, the door must be open

2. if the keycard is invalid...? we only know if the keycard is valid

3. If the door is shut, then the keycard must be invalid

🚨 Spoiler alert if you haven't solved this puzzle yet!! This statement is part of the "DOOR OPENS → KEYCARD IS VALID" group

I see that DOOR OPENS → KEYCARD IS VALID = if the keycard is invalid, the door is shut.

But I thought I was doing something correct by nullifying that as an option in #2 because it negates the sufficient? And I'm not clear on why #1 Door Shut → Invalid Key and/or its contrapositive Valid Key → Door Open isn't the answer.