In Avengers: Endgame and Captain Marvel movie, we have seen that Carol Danvers is one of the mightiest superheroes. The most important power she posses is the power of her enemy. For example, if she goes and fights with Thor then she will have the power of lightning inside her as well. So, it was pretty obvious for many to wonder as to why Captain Marvel didn't use the Infinity Gauntlet herself.
Avengers: Endgame final battle scene:
At the end of Avengers: Endgame, there is this cinematic battle going on. Through the entire course of the battle, we see how Thanos is trying to get his hands on the gauntlet made by Tony Stark.
At one point in the battle, we see Captain Marvel rescuing Peter Parker who is holding the gauntlet. At the precise moment, we see Danvers holding the gauntlet and it made many to ask as to why she didn't wear the gauntlet and snapped the infinity stones herself rather than taking it to the van where Ant-Man was waiting with the time machine.
Tony Stark ends up putting the gauntlet on later and ends up dying because of it. Based on Captain Marvel's powers, she was strong enough to serve the effects of using the Infinity Stones.
Avengers: Endgame Director Joe Russo explained this pretty well in an interview that "Captain Marvel can also withstand all the power of Infinity Stones at once. The reason we choose to let Iron Man do it, in the end, was that he was the closest one to Thanos at the time."
As per the latest theory, the main reason why Captain Marvel didn't use gauntlet was because of Professor Hulk's reverse snap.
After all the Avengers assemble the Marvel's Infinity Stones, Professor Hulk wears the gauntlet and do the reverse snap to bring everyone back. In this process, the gauntlet literally and figuratively becomes unfit for anyone else to wear. With the gauntlet in its mangled physical state, incapable of resizing itself, and all of the people brought back from the effects of the first culling, no one possessed the physical opportunity to wield the Infinity Stones.
Why Tony Stark used the gauntlet?
Now the next question arises if this was the case then why Tony got to do it? Well, Thanos himself once said, "The hardest decisions require the strongest wills," and Tony has seen first hand what Thanos and his army can do. Out of all the Avengers, he had one of the strongest wills to eradicate the alien race from the universe.