Frankly, there is precisely one reason. It is another ammendment to the constitution, the forth, which protects against unreasonable seizure of property.
Had the government banned weapons prior to the cutoff date, they would have had to compensate the current owners; just grabbing the guns would have violated the forth amendment. Had they just restricted them to the people who already owned them (keep what you have but you can't get rid of it), that too would have violated the forth amendment, because it would have rendered the property worthless (you couldn't sell it).
So they grandfathered the existing Class 3 weapons.
The second amendment does not guarantee the rights of the people to ANY weapon they choose. Hence, you can't (as someone suggested) own a tank, cannon, or atomic bomb. Such bans don't violate the second amendment. (or so goes the legal theory).