He's a coward in many ways. He ran from Heaven when he couldn't take it anymore, but didn't have the balls to actually Fall, so he took an alternative route and hid himself from his family. He avoids confrontation and when he can't, he uses conjured proxies to fight his battles for him. He's horribly afraid of his family, both because he's afraid they'll kill him and because he's afraid that they'll see what he's become, look down on him in scorn, and just take him out and he can't stand the thought of being looked down at by the people he loves more than anything. Despite his cowardice, he's not actually afraid of very many things, which has a lot to do with being an archangel and generally being more powerful than most things and even when frightened, he adamantly refuses to show terrified he is. You'd have to be stabbing him to death before he'll show his fear.

Gabriel's most obvious fatal flaw is own arrogance and overconfidence, while he can generally handle any threat, he has a tendency to miss the bigger picture and doesn't consider alternate means of attack, beyond the obvious, so when people get the jump on him, it's usually because they turned his tricks back on him and as soon as he thinks he has all the cards in a situation, the trap is already sprung. The Winchesters have pulled this tactic on him twice now and Kali pulls it on him in HotG- the easiest way to lure Gabriel in is to make him think he's winning until the last second. He's not stupid. He's a product of an overinflated ego and a stubborn attitude that has him repeating mistakes, BECAUSE WHAT ARE THE CHANCES ANYONE'S GONNA PULL THAT AGAIN? REALLY?