Liverpool submitted their request to postpone their match against Arsenal before even receiving their round of ‘positive’ tests, according to a report.

The Athletic report that when Liverpool submitted their request to postpone the League Cup semi-final second leg, they didn’t yet know the results from their additional round of testing.
That additional round wasn’t necessary to play the match in the first place, given Liverpool had already received a round of negative lateral flow tests. But they took the additional tests anyway, to make sure.
Whilst that’s an understandable stance, it’s rather bizarre to request a postponement when the only information you have is a round of negative tests.
When the additional tests came back, they came back positive, which was an error. The players didn’t actually have Covid, but something had gone wrong with the independent lab testing.
All the same, it was enough to get the game postponed, as the faulty tests couldn’t be invalidated in time.
When those tests were invalidated, neither Liverpool nor the authorities made that clear publicly. It was only when Jurgen Klopp mistakenly suggested they’d received “false positives” that suspicions were raised.

All in all, it’s just a bit of a mess. At the time of their request, Liverpool didn’t have any reason to postpone, and in hindsight, Liverpool didn’t have any reason to postpone.
But for the crucial period in between, the faulty tests made it look like they did.