it's basically the same reason in the book. He's just absolutely terrified. Enough that he would rather die horribly on earth than in space

It's been a while since I read the book. But I remember Grace thinking of himself and his actions with shame. He was selfish and a coward for not wanting to sign up for something with only a small chance of success. And even with success meaning he would have to die in space. It isn't that he wants to stay on Earth, which is rapidly becoming a shittier place every day. But he'd prefer that over going on the mission.

I don't know if calling it believing in himself is the right way of describing it tho. He obviously doubts he is the right man for the mission, but at the same time also has a physical reaction to the thought of going on a suicide mission. A mission where the best case scenario is that he dies. I would describe it more as a lack of character, something which he turns around in the end and finds the strength within he didn't know he had.

In the book Stratt makes a pretty convincing case, Grace admits this. But he chooses not to go, only for the issue to be forced. This part was done much better in the book than in the movie. Like another commenter said, in the movie it's treated almost as a joke. Instead of the absolutely horrible situation it actually is. And in the book we also get a lot more insight into Stratt. She cares for Grace in a way and feels for him, she understands his reasoning and also accepts this puts the burden on her to make it happen. She was chosen because she can make these kinds of calls, with the ends always justifying any means.