Because he's just a kid from Brooklyn.
When Tony Stark said "everything special about you came out of a bottle", he didn't know what he was talking about. Captain America isn't special because of any serum, but because it's Steven Grant Rogers standing behind that shield. Steve is willing to give everything he has for what he believes in. Steve stands for equality and freedom. Steve, who would rather protect people with his shield than kill anyone. But he'll make the hard call if he has to.