this happens a lot in the shop. Force it in.
Sounds like bad advice, I know, but the threads of the plastic cup deform a bit as you screw it in and it feels like you've bottomed out in the BB shell, so just keep cranking on the left cup and a few turns after you swear you've messed something up and the cup will free up and spin into position normally.
You won't mess anything up doing it this way. Even though it sounds scary, the plastic cup threads would be the first and only thing to screw up in the event I was lying to you

Don't ride with the cup sticking out that far. depending on how little thread you have engaged, you run the risk of slipping the cup on the left which will, in turn, totally trash the BB threads on the right. Also, you won't have adequate preload on the right side, which may allow the fixed cup to back out of the threads, leading to similar damage.

BTW, this is based on installing literally over a hundred of these units.