I can think of two good reasons. One, perhaps he's not a lunatic who starts shooting at people before he's sure what the situation is. Two, when you feel threatened it's not a good idea to give away what your main defense is until it's time to employ it.
"I'm a black man and I'm pulling the gun before he gets to my car," Matthews said.
You said it, Matthews, not me.
3. Perhaps he let he guard down, thinking that he was in a civilized community and when confronted with a deadly threat reacted in an appropriate manner saving the life of the young lady and himself.