Surely the aerodynamics are better for firing a missile backwards.

If you fire it forwards, the missile has to accelerate through whatever air resistance you're both already experiencing through even more air resistance to get to the target. That's hard.

If you fire backwards, the missile uses air resistance to accelerate towards (i.e. slow down) towards the target. Even when it goes through 0mph relative to the air and continues to accelerate, the resistance will be much less as it approaches an even higher closing velocity in a shorter period of time.