brave, not selfish, legitimate leader, prompt to sacrifice
The same can be said about Tony Stark aside from the not selfish part. He's brave, Tony's usually the first to face off against an enemy. He's a legitimate leader, he's actually the one who rallied the avengers to Cap's side in the first movie. He's also prompt to sacrifice. Remember who saved all of New York and all of the Avengers from a nuclear blast?
But more to your question. This version of Captain America isn't the same as his comic book counter-part. In the comics, Cap is perfect, or as close to perfect as he can be. In the MCU, this isn't the case. Sure, Steve is a very good human being, but he suffers from major flaws. He's extremely arrogant, almost on Thor's level from the movie Thor.
In the MCU, it's clear that Steve considers himself better than every other human on the planet. Some of his lines from the Avengers shows that. "Big man in a suit of armor, take that off and what are you?" This line alone is incredibly insulting. He's not only telling Tony that he's nothing without that suit of armor, but basically that anyone Steve feels is beneath himself is nothing. It's the equivalent of saying something along the lines of "Oh, you never served your country or gave back to your community? You're beneath me."
Again, yes, Steve is brave, heroic, and selfless, but these qualities aren't what make someone worthy. Remember, Thor had those same qualities, as does Tony(aside from the selfless part). What made Thor unworthy in the first Thor movie was a combination a a few things. His arrogance, dude thought he was untouchable, better than everyone else on Asgard, and above the law due to his heritage. Cap is almost just as arrogant. Thor also wasn't humble in the beginning. He never recognized others for assisting him, it was always his achievements, no one else's.
Cap is also extremely self righteous. Watch most of his arguments or confrontations with anyone in the movies. In his head, he's always right, it's his way or the high way and if you don't agree with him, you're wrong, end of story. This is evident by his guilt tripping of Bucky in CA:TFA. Yes, Steve was trying to do his part to help the country, but he flat out made Bucky feel like shit for trying to dissuade him from enlisting.
Bucky was trying desperately to save Steve from embarrassment, prison, and probable death. Bucky was being a good friend and even suggested other ways Steve could help the war effort, something Steve actually scoffed at(again, even before he went through the Super Soldier program, he thought he was above certain people and certain things). Like I said, he made Bucky feel horrible for trying to protect him, all because Steve felt he was right and above working in a factory to produce supplies for the troops.
Steve: "What do you want me to do, collect scrap metal in my little red wagon?"
Steve: "I'm not going to go sit in a factory. Bucky, Bucky, come on, there are men laying down their lives. I got no right to do any less than them. That's what you don't understand, this isn't about me."
Bucky: "Right. Because you got nothin to prove."
This dialogue clearly shows that Steve doesn't believe that doing something like this is worth while. Sure, his words can be considered patriotic, but Bucky sees right through him. Steve's motivations to join the military are entirely self-centered. He feels he has to prove something to the whole world. He's basically saying,
"You want me to join the women folk making weapons and shoes while all the men go out and fight? Phhp. please, I can fight just as well anyone else, just watch." In face, we can add a few more unworthy qualities based on this alone. Narcissistic, self-centered, sexist....I'm sure there are many more that can be added, but I think we're around a half dozen traits that would make MCU Steve unworthy.
Now that I think about it, MCU Captain America is actually a douchebag, even more so than Tony Stark or Thor.
Steve's arrogance shows multiple more times in the movie. Ordering Col. Phillips to give him names and information, you're a Captain dude, not God. Again, The hell I can't, I'm a Captain. Pretty sure Peggy Carter's position was much higher than a newly promoted Captain.
His self righteousness is on full display in the Avengers as well. In the scene where he discovers that SHIELD is using the Tesseract to make weapons. He blatantly doesn't care that Earth's weapons are nothing compared to people like the Hulk or Thor. He doesn't care about the fact that if the Hulk were to go on a world wide rampage, that no one could stop him with their current weapons. Or if Asgard or another civilization were to attack Earth, humanity would be utterly defenseless. None of that matters, all that matters is that SHIELD is using an energy source to make these weapons. Nevermind the fact that it can advance humanity. All Steve saw was HYDRA weapons and designs and remembered what they could do. Even Fury's explanation as to why they were using the Tesseract went through one ear and out the other. To Steve, he was right, period, end of story, humanity's defense be damned.
These are the glaring reasons why Captain America is not worthy to wield Mjolnir in the MCU. He's extremely arrogant, self righteous, narcissistic, self-centered, sexist, prideful, and thinks of himself as above everyone else. These are the exact aspects that made Thor unworthy to wield the hammer in the first Thor movie. It wasn't until Thor dropped his pride, arrogance, self righteousness, and accepted his own humanity that he was able to re-wield Mjolnir. I imagine by the beginning of Age of Ultron, Cap will have started to lose his arrogance, pride, and self righteousness, which is why he's able to move the hammer, but not yet pick it up.