Why don't fighter planes have guns that fire backwards?

WW2 Aircraft having gun to fire backwards

Guns on today's fighter aircraft are not for dog-fights.  They are there for ground attack where CAS (Close Air Support) are needed.  Today's jets are simply too fast and maneuverable to be good gunnery targets in a close in dog fight, assuming the shooter didn't take out the target with a missile at 20 miles.

So supposing you did have someone on your tail and you DID have a rear firing gun.  What then?  Think of reversing your car at high speed and trying to keep the road centered in your mirror.  The slightest twitch of your jet would send any bullets off target, and twisting/turning is the best dog fight defense you can have in a gunnery dog fight. 

You would need a turreted gun with tracking radar and perhaps a second crew to man it.  Too heavy a penalty for a very rare usage.  In short, rear facing guns are simply impracticable on today's fighter jets.

ANOTHER REASON:

It is not that big of a deal to mount a rear facing gun on a fighter jet but how would he cue his rear sights to tag the hound, might need an auto turret but all that could be done too if the energy of the bullet won't be reduced to (minus the forward m/Sec) less than half. So in this case if the forward range is let's say 2nm then the same gun rear facing might have an effective range of less than a mile. And no one chasing you would wanna get that close anyway to avoid being hit by your debris. I think a shotgun like chaff repeater would be quite helpful to knock closing in missile or may be to leave some FOD trail and scare the guy trying to kill you with his gun. This skunk gun could be mounted but it's use might not be worth the extra weight. Most Russian and European fighters (front shooting guns) carry 150-250 round mags, but only the American fighters carry over 500 rounds for the classic dog fights. Dog fight isn't dead but most attackers try not to engage in one, or might have a formation of escorts to deal with any interceptors to complete their attack, there's lots of warning time due to aew&c in the air so no side would be surprised. With all the modern electronics giving early warning, kills the surprise and hence making attack more difficult, that's why the USAF & Navy want some magic stealth fighter bomber to take care of the early days of a war to do SEAD missions and then unleash IMAX platforms. Since the end of wwii there has been no conflict among equal powers equipped with modern arms, so most of the R&D and exercises and hypothetical scenarios haven't been put to real test. A limited air conflict over Eastern Europe or South China Sea would expose most of the myths about modern air warfare. As long as we don't see something like that, we might be fooled by the military industrial complex to buy their new gadgets.