SPOILER QUESTION: Why did Hulk refuse to come out in the Avengers: Infinity War?

All the speculations can stop now.

Hulk is not scared. He is never scared of a good fight.
He started an attack on Fire Lord Surter ALONE, enlightened with the Eternal Flame.
He did not even think about it. He just leaped to the crown of Surtur.

The Russo brothers have finally given an explanation of the Hulk scenario.

Hulk does not want to come out because Banner always uses him.

Examples:
Avengers - Banner wanted to help the team against Loki, he gets the Hulk out.
Avengers 2 - Same scenario while attacking Hydra bases, last one was Black Widow.
Thor Ragnarok: That big stupid dog won’t die. Banner finally gives up on not being Hulk and jumps out to save the day.

Hulk is really mad at banner because Banner lets him out only when he needs him to save his/others ass. And Hulk does not want to be just a helping hand to Banner any more.

Most people think that Banner is Hulk and Hulk is Banner.
Which is not the case.
Banner and Hulk are two different personalities sharing the same body.

In Thor Ragnarok when hulk turns to Banner. Thor and Banner are sitting on steps and Banner is explaining Thor about his situation with Hulk.

“Each one had one hand on the handle. But this time it was like Hulk had the keys to the car and I was locked up in the trunk.”

This is Banner’s perspective.

But remember majority of the time Hulk is not let out by Banner.
Hulk feels the same what Banner felt those two years on Sakar. Locked in the trunk.

That’s what the story plot is going towards for Hulk.

Feige already said this “Hulk/Banner will have his own movie arc in Thor and Avengers movies.” as Universal won’t allow for a standalone Hulk movie.

So the movie plot is Banner and Hulk figuring out how to stay together.

Remember Hulk and Banner are in constant fight (mentally). And even in such a situation Hulk is the strongest there is.
Now just imagine when they both decide to work together what can Hulk do.

Banner’s seven PhD’s and Hulk’s smash i.e Professor Hulk (in comics)

Edit 1 - Also whenever Hulk saves the day, it’s Banner who is appreciated not Hulk.
Everyone hates Hulk (on earth). That’s why Hulk was enjoying his life on Sakaar. He was the champion, people loved and feared Hulk and he could be just himself.

And because Banner decided to help Thor, they are back on earth where Hulk does not want to be. So once again Banner does what he wants to without considering what Hulk wants.

Thanks for the edits:- Nahush Shrivatsa, Andrew De Jesus, Jason Marriott, Katie Anne Holton