... used bike ...

In one shift direction, the derailleur is moved by the shifter pulling on the cable ... which sometimes can overpower sticky cables.
In the other shift direction, the shifter simply releases cable. It is up to the derailleur spring tension to pull the cable back in order to make the shift.

If there is not enough spring tension to overcome the cable friction (ie weak broken spring or large amount of cable friction), the derailleur will not shift correctly (or not at all in that direction).

Do like the other posts have suggested. Check for cable friction and check for derailleur spring strength/function.