Layups are missed because of a player's lack of concentration, and their failure to put the ball off the glass at a the correct angle. Often they rush their shot in fear of having it blocked. They have to be coached to not worry about getting it blocked. Some times it's going to happen. 90% of the time it won't.
EVERYBODY that plays basketball is going to have their shot blocked at some point. 7 foot post players in the NBA got/get their shots blocked, some times by players smaller than them.
Wes Unseld at 6'6" blocked a lot of shots by opposing post players during his career, most whom were taller than he. However, most of the time, he didn't.
Very very seldom will a player block a lay up/put back and not foul the shooter. That's where Liv has picked up a lot of her fouls the past 2 years (fly swatting). When going up for a lay up, you have to put EVERYTHING out of your mind for 3-4 seconds, and concentrate on where you're going to put the ball off the glass. If it gets blocked, so be it. But if it doesn't, its got to go in.
It's NOT hard to miss a put back because of the traffic or number of opposing players around you ALL trying to block your shot. Many times, rushed shots will not go in. You're just trying to get the shot off without getting it blocked, especially if there's someone 3-5 inches taller than you (in a different colored jersey) in close proximity.
Aaliyah missed a put back Saturday that didn't draw iron. She rushed the shot. That's one of the many things I like about Aaliyah, she makes her bunnies, free throws and put backs.