Current is about conservation of charge. We know that charge is conserved, so current is about telling us how this conserved thing changes. If the charge is increasing in some region, then by conservation of charge, there is a current flowing into that region.
Suppose that we have two spheres connected by a wire and electrically isolated from everything else. Now, if the right sphere becomes positively charged then by conservation of charge the left must become negatively charged. So, we want to DEFINE current as a flow of charge from the left to the right, to reflect that conservation of charge.
Now, let's look at how the right sphere could become positively charged. You could have positive charge carriers move from left to right, so the current would be in the direction of motion. However, you could instead have negative charge carriers move from right to left. That would still accomplish the end point of having a positively charged sphere on the right and negatively charged sphere on the left, and in that scenario we have DEFINED our current to go from left to right, so the current is in the opposite direction of the motion the charge carriers.