Here's an article about it. The tl;dr is: test pilot shoots at ocean, kicks in afterburners, bullets start out faster, but slow quickly. They reunite in mid-air and sparks fly.
What I don’t get is… I mean, the relative speed difference between the bullets and the plane just doesn’t seem like it would be enough to cause them to rip through the plane as if the plane was shot on the ground from a dude with a gun or something.
He shot the bullets, then tilted down a little more and hit his afterburners. He had to pull up so not to continue on to a salty grave and his parabolic trajectory and the bullets surprised each other. So, a pinch of the bullets slowing significantly and a sprinkle of the plane speeding up.
The Tiger gained the dubious distinction of being the first jet aircraft to shoot itself down. On 21 September 1956, during a test-firing of its 20 mm (0.79 in) cannons, pilot Tom Attridge fired two bursts midway through a shallow dive. As the trajectory of the cannon rounds decayed, they ultimately crossed paths with the Tiger as it continued its descent, disabling the aircraft and forcing Attridge to crash-land the aircraft; he survived with a broken leg and multiple broken vertebrae.
From Wikipedia
I think just saying that it hit itself due to its high speed doesn‘t really tell the whole story.
That sounds like bullshit though, the bullet would have the same speed when released from the shell in addition to speed generated by the blast in the shell. Did the plane fire and then accelerate enough to catch up to the bullet? That's pretty convoluted and unlikely, you would have to actively try to shoot your own plane.
EDIT: The dumbass shot at a slight down angle and then engaged the afterburners. Skill Issue.
Yeah, the initial velocity of the bullets would be the sum of the plane's velocity plus whatever velocity the bullets gain coming out of the barrel.
But, what apparently happened is perfectly believable (if extremely unlucky). It's not that the F-11 was faster than its bullets, it's that it flew in a way that its path intersected the path of the bullets it had fired. As soon as the bullets left the barrel they would have started slowing down, eventually ending up on a ballistic trajectory. The F-11 would have stayed at approximately the same speed, but if the pilot hit the afterburners it would have sped up considerably.
Still, the likelihood of the speeding up plane hitting the slowing down bullets is extremely low.
Imagine the fear and shock of test firing your guns into the water, speeding up and moving on, then suddenly your aircraft is shredded by a seemingly invisible force.