It’s a common contrail. The object is traveling toward you, not away from you, and since the contrail has a long persistence, it looks like it emanates from the horizon, thus the illusion that it is a missile traveling away from you.
Seems pretty clear to me.
Since it's so common, I assume you will be able to take a picture similar to the ones we've see and post it for all to see just how common it is. I've lived in the NYC metro area most of my life. The only thing I've seen live that even approximates the video from LA is a Space Shuttle launch. I'm also a pilot (albeit inactive now). I've never seen anything like that in the air either. (And if you haven't flown in a major metropolitan area like NYC, you just cannot imagine how attracted your eyes are to anything in the air that is moving while flying approaches and departures.)
ML/NJ