Why didn’t Captain Marvel put the gauntlet on?

Although, Julius has answered it pretty well and it is correct, I'd like to add words from director here.

As Joe Russo explains why Captain Marvel didn't put on the Infinity Gauntlet,

Q: Why Iron Man has to be the one to do the final snap, couldn’t the people like Thor, Star-Lord or Captain Marvel whom all previously have handled the power of Infinity Stones done it instead?

A: Thor in this movie couldn’t do it, only Hulk was strong enough to do the snap without dying. We are still not sure whether 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 because he was the closest one to Thanos at the time. In all the futures Doctor Strange foresee, Iron Man was the only one who could get close to Thanos and do the snap. People usually think the death of a hero is a horrible tragedy. But we think this is different. When his death was able to bring back hope, to save half of the universe, then his death was powerful and meaningful. We shouldn’t feel too sad or angry about it.

So, they only let Iron Man do it because Iron Man was close to Thanos and can do the snap as foreseen by Doctor Strange.

I wondered this, too. I think Captain Marvel is strong enough to use Stark's gauntlet. Her powers came from the Tesseract/Space stone, as seen in her MCU origin story.

One possible answer as to why she didn't use the gauntlet is that she simply didn't think of doing it. This happens once in a while with Marvel characters. In Infinity War, while discussing how Vision's neurons/synapses and Mind stone were set, Shuri asks Banner, "Why didn't you just reprogram the synapses to work collectively?" Banner responds, "Because we...didn't think of it."

A second possible reason - had Captain Marvel put on the gauntlet, it would have taken about 5 to 10 seconds for it to "boot up" and be snap-ready. Those valuable seconds would've given Thanos or one of his minions time to get to her and wrest it from her. Getting into the quantum tunnel in the van was the much faster solution, and getting to any solution immediately was key to the Avengers winning. But even then, she wasn't fast enough - Thanos was quicker with his weapon. Now this makes me wonder if Quick Silver had to die (in Age of Ultron) so that no one could successfully get to the van, or do anything super fast. Hmm.

I actually think really powerful characters like Captain Marvel, Doctor Strange and Wanda still wouldn't survive snapping the Gauntlet themselves because they still have human bodies. I mean, we saw Captain Marvel fight Yon-Rogg in her movie without using her powers and just her raw strength and she got her butt beat, so possibly her physical body wouldn't handle the snap then. It seems that her binary powers are what makes her that powerful, but "raw strength"-wise she is nothing. But that's just a theory.

Hulk, Thor and Thanos seem to be the only ones who could survive using the Gauntlet. Thor is God, Captain Marvel is just a mortal human with powers, like Wanda and Strange.

Another explanation is that she doesn't understand how the gauntlet works. She's never been there to see Thanos or Hulk use it, and doesn't understand the risks to her life, or that using it is as simple as a birthday wish. In the heat of battle, might make more sense to deliver it than figure it out.