As has been pointed out, in the real world, the CAP theorem comes down to "do I choose to offer service to everyone in the presence of a partition?"

Consider a replicated database. A replica that's partitioned from the others cannot receive or propagate updates and will become inconsistent with those on the other side of the partition.

If you allow that node to stay up, you're sacrificing consistency for availability; and you're "AP".

If you force that node down, you're sacrificing availability for consistency; and you're "CP".

In principle, you can choose "CA". That's equivalent to saying "I choose to offer no service at all in the presence of a partition", so that's kinda sorta strictly worse for most workloads than "CP" and therefore uncommon in practice.