You’ll notice that on fighter planes, the nose cone of the plane and missiles are all some form of Ogive tangent or Von Kármán variant pointing in the direction of travel. The shape of nose cones is massively important as you’re balancing drag and stability (and more) in sub- and super-sonic flight. The aerodynamic characteristics of a missile are important in both it’s effect on the plane when mounted and it’s ability to detach, accelerate and maneuver when fired.
To have a rear-facing missile mounted to a fighter’s wing, it would need some sort of “butt-cone” attached to the rear end of the missile, facing in the plane’s direction of travel. With the extreme acceleration rocket motors achieve overcoming the delta-V of the plane is not an impossible task, but you would need to scale up the rocket motor to overcome this negative velocity (call it f(orward)-V) start and some truly amazing flight control system to keep the missile steady as it’s flying backwards (r(ear)-V).
The missile is launched with a f-V equal to the speed of the plane. It’s accelerating at r-V, determined by the (rather large) rocket motors installed… I don’t know the exact speed these missiles accelerate, but considering their size and lack of pilot, I imagine they pull some HARD acceleration…
So again, missile is launched, f-V equal to plane speed, r-V equal to rocket motor impulse, accelerating towards the point where f-V and r-V cancel each other out and the missile, momentarily, would have zero speed relative to the earth and then would continue to accelerate towards the target.
Considering the speeds involved in a dogfight, the time the rear-fired missile would take to a) not fall out of the sky while whizzing backwards and b) start accelerating from zero towards the target, it best be a couple few many kilometers away for this missile to get it’s act together.
The mode of failure would definitely be in the “whizzing backwards” part of its flight… the entire missile would have to be designed so the fins work in both directions of flight and be capable to keep it aloft as it has a speed graph that looks like an AC sine wave.
MinutePhysics on YouTube did an excellent video that (partially) applies here… why it’s so hard to get to the sun from earth !!! All about rearwards velocity and overcoming it, do scope it out… https://youtu.be/LHvR1fRTW8g
I hope this helps some… this is my first post here so be gentle