Doc Daneeka, Yossarian's friend and flight surgeon, is marked by his complaining. His tagline is "you think you've got problems. Well I" blah blah blah. His so-called problems are pretty tame compared to those faced by the enlisted men. All he worries about is his temperature – which is the same all the time – and logging his flight hours, which Yossarian helps him fake. Despite Yossarian's generosity to his friend, Doc Daneeka never reciprocates. This seems to be a recurring theme, doesn't it? Because Doc Daneeka fears flying, Yossarian logs him as completing flying hours when he's really not. However, Doc Daneeka never even considers taking Yossarian off active duty to repay him. In fact, he straight up refuses Yossarian and tells him that Catch-22 makes it impossible. Doc Daneeka is something of an ingrate.
His selfishness and ungratefulness prove to be his undoing. Because he has Yossarian falsely enter his name on the McWatt's flight log, everyone assumes he is aboard McWatt's plane when the pilot commits suicide. This means that Doc Daneeka is dead on paper. Actually, he's quite alive and tries to demonstrate this to all the men and his wife. However, politics get involved. The men resent him for giving Colonel Cathcart a reason to raise the required missions, and his wife profits from his supposed death and thus refuses to acknowledge that her husband is alive. When all is said and done, Doc Daneeka realizes it doesn't matter whether or not he still breathes; when everyone treats him as an outsider, he's effectively dead. At this point, he becomes more isolated from the men and more embittered. He becomes yet another symbol of loneliness and alienation, but – unlike the chaplain and Major Major – the fault is completely his own.
One thing Doc Daneeka has going for him, however, is his sense of duty. During sieges, he performs admirably, tending with care to the wounded. During Milo's bombing of Pianosa. He does not flee. Instead, he stays on the dangerous grounds to care for the men. But he's not just a selfless angel. Like many other characters in Catch-22, he is partly motivated by fear. In every man's wounds, he sees an omen of his own death. This may be why he is so bent on healing others – it's a misguided belief that he is really saving himself. It is also implied that the Doc thinks Milo is wrong for bombing his own base. He mutters seditious things about him until he is bribed into silence by Milo's gift of a garden chair.
So to make a long story less long, although Doc Daneeka performs his duty, his goodness is quickly negated by his greed and laziness.