The problem isn't who to target first, it's knowing who and when to swap targets.
It is perfectly fine to attack the tank at first, just don't waste your CD's on him! Talk among your team and determine which enemies are dangerous or which ones you can most easily kill.
Having your team focus their damage is crucial, and making sure that your team doesn't hold their targets when the ADC dives into the fray is often a deciding factor in battles.
The tank needs to know when his team can't initiate on the enemy ADC and APC as well so that you can back out of bad initiations.
Those with CC need to manage it as a resource to save the team and secure kills, those that deal damage need to know who they can/are going for.
There are a lot of things that take place in team fights.