That's because nobody will sell you an F-15. You can buy a MiG-21 for a song though
The constitutional justification is that it's a weapon suitable for arming a militia and ensuring the security of a free state- not hunting, recreation, or even personal defense. In fact, there's no constitutional justification to own a gun for recreation or hunting!
He went on, in a FaceBook interview, to point out the shotgun is a lot easier to defend yourself with. In other words, it's more dangerous. If it is, why not ban those instead? However, it isn't- a carbine is FAR easier to shoot accurately and easier for most people to handle, especially smaller people.
The AR-15 is not automatic, and I believe we DO have a constitutional right to own an automatic as controling them is an infringement on my right to bear arms, and congress has no constitutional authority to enact such a ban.