At first look, Captain James T. Kirk of the USS Enterprise was fearless. One glance at the daredevil spark in his eyes and the carefree smile on his face was usually enough to convince most people that the man wasn't afraid of anything, and that nothing the universe threw at him could scare him.
To some degree, it was true.
Kirk wasn't afraid of many of the things normal people were afraid of. He had blatantly told anyone who asked that he wasn't afraid of death whatsoever. Anyone who served with him for very long was able to see that he was good at keeping his head in normally terrifying situations. After his many close-calls, he always seemed to bounce back with little to no problems despite the harrowing experience. In all appearances, the young captain really was fearless.
However, to those who knew him better, they could tell that he had just as much fear in him as anyone else. The captain's fear was simply more pinpointed to several things instead of the wide range of fears most people had. The lack of variety also meant that he feared those things much more deeply, to the point where they were almost phobias, in a sense. He didn't fear public speaking, spiders, heights, or anything that was fairly common like those things. What he feared couldn't even be touched, much less seen. Because of this, it had taken awhile for the crew to notice what he feared, but they figured it out eventually.
The captain feared being alone. Despite the fact that he was very independent and naturally inclined to be more of a loner, he could always be found in a crowd – even if it was a crowd of strangers. Sometimes he would flat out ignore the crowd, simply immersing himself in their presence as he did his own thing. Once after consuming numerous drinks he had even admitted that he sometimes he picked up women just so that he wouldn't be alone at night.
Another fear of the captain's was failing. This fear was a little harder for the crew to figure out, but enough subtle moments eventually gave them enough information to notice. There was the Kobayashi Maru back at the Academy, which Kirk had taken three times despite nearly everyone giving up after the first time taking the test. The crew knew from various conversations that Kirk had become obsessed with the program, and that he would have refused to give up until he won. Luckily for everyone who knew him, he had passed the test the third time around.
Connected to his fear of failure was his fear of disappointing those he cared about. When he was in charge of the ship, he made it a point to know every detail about the crew and their jobs. He was attempting to understand everything he could so that he was less likely to disappoint them through his ignorance. Sometimes it seemed like Kirk knew more about them than they themselves did, so eager was he not to fail.
The fear that was probably the most prominent was his fear of losing something he considered his. From the way he treated his possessions, it was clear that once he considered something his he was very, very unlikely to let it go without a hassle. The things that mattered most to him were well protected and well taken care of even as they were cherished. He considered the things that mattered to him priceless, and would barely even consider parting with them unless something that mattered even more to him was threatened or offered.
In a strange way, the crew had somehow become his as well. That's not to say that they were considered or treated like objects, but that they were treated as his. Honestly, they didn't really mind. Like with everything else Kirk considered his own, he went out of his way to protect them and make sure that they were happy. It was evident to anyone who cared to look that they mattered to him a lot. From the looks he gave potential threats, it was also evident what would happen if any of them were harmed.
From his reactions with Nero and Khan to his responses on away missions turned sour, it was clear that he would give anything to make sure that they weren't taken from him, even if it meant sacrificing his life to make sure of that. Needless to say, that way of thinking was rather frustrating to deal with when many of them felt the same way.
They knew that he feared losing them, but the sentiment went both ways. The captain was as reckless as he was caring – especially when trying to protect his own. It was entirely possible that they would one day hear the announcement of their captain's death once again, and that the next time that happened he wouldn't come back.
But they all knew that when it came down to it, not a single one of them would be able to stop the captain from being reckless and relying on minuscule odds to get him through conflicts. So, they did what they could to ease his fears while crossing their fingers that the next mission wouldn't be his last. If it meant carrying a survival kit every time they left the ship, so be it. If that meant always carrying a backup communicator, then that's what they would do. If it meant every crew member would be trained in self-defense and required to carry a small knife in their shoe, then that's what would happen.
The captain may look fearless, and he may even act fearless, but he was just as mortal as everyone else, and everything mortal fears something. Kirk's fears might be intangible, but that didn't make them any less real. It simply meant that they would have to work a little harder to lay them to rest. That didn't matter to the crew though. They're captain was worth the extra effort, and he would do the same for them in a heartbeat.
And if the captain had no idea what they were doing, well, that was just a bonus now wasn't it?