The Battle Master fighter's Precision Attack maneuver states the following (PHB, p. 74):
When you make a weapon attack roll against a creature, you can expend one superiority die to add it to the roll. You can use this maneuver before or after making the attack roll, but before any effects of the attack are applied.
Is there ever a reason not to wait until after the roll has been made to use the maneuver?
As explained by the Hobgoblin, it is (almost) always better to see the result of your attack roll before you decide whether or not to use Precision Attack. However, suppose you are trying to manage the outcome of an attack, and in addition to Precision Attack you have another ability that affects the attack roll, but only if it is used before the roll. Further suppose that this other ability is more valuable, or has a higher opportunity cost to its use than Precision Attack. In this case, you might want to know the result of the Precision Attack roll in order to decide whether or not to use the other ability, but if you wait until after the attack roll you will be unable to use the other ability.
Clearly that is a very specific case. As one example, suppose your party has both a Battlemaster and a Divination Wizard with Portent (or even that one multiclassed character is both). You start the day with 4 combat superiority dice but only two Portents. Further, given the possible uses to which they might be put, it is clear that Portent is the more valuable of the two resources such that if you have a choice to spend one or the other, it is better to use the combat superiority die and preserve the Portent.
A combat starts against an opponent of known AC and for some reason it is very important that the opponent will be hit by your attack. Given their AC and your attack bonus, a poor Precision Attack roll (plus a random attack roll) would have an unacceptably high chance of failing to hit them while a good Precision attack roll will have a more acceptable chance of failure. Changing the attack roll with a Portent would guarantee a hit, but this can only be done before the roll. In this case, you might reasonably decide that it is worth it to spend the combat superiority die beforehand - if it is a high roll, you can preserve the Portent for later use, while if it is a low roll, it would be better for you to preemptively replace your attack roll with a Portent rather than risk your attack missing after a low attack roll.
In a similar situation, as suggested by @StephenTG in comments, you have a Portent that is close to hitting, but not quite. A high Precision Attack would make the difference, but a low one would not. In this case, you might roll the combat superiority die first to see whether a hit will be guaranteed if you spend your Portent, or whether the attack will fail even with Portent. Here, using your Precision Attack gives you all the information you need to make the optimal decision, but only if you do so before the attack.
If you decide to expend the die before the attack roll, you forgo the information that roll gives you. For example, if you roll a natural 20 on the attack roll, you always hit, so there is no need to expend one of your superiority dice. Waiting until you see the result of your attack roll always gives you better information to make the decision to spend the die, or not.
One possible argument could be speed of play: if you spend the die in advance, for example you know you are fighting an hard to hit opponent, you can just roll both dice together, and add them up, so there are no two rolls and the slight delay that brings. You cannot roll both and then decide, because if you do roll both, you also know the result of the superiority die roll before deciding to spend it, and could only then take it if it adds a lot.
Another super fringe case might be if you are worried about an enemy taking mental control of you and then using your resources against you, so you try to spend all your powers as fast as you can as long as you still can -- but that would be an exceedingly rare situation.
