The simple answer is because that's the way THEY WANT IT, and that ALL we're being offered.
They NEED a registration of all guns, so they can answer the question "PROOVE you had a background check done ON THAT GUN",, which to my mind is a question that should NOT be asked.
Their entire concept of tying the background check to the specific gun (by ser#) is only needed if the desired end result is to create a registration list of guns. (Along with the repulsive base concept of assuming guilt and having to have the gun owner prove their innocence ).
They could run the check only on the person, but they don't want that, and won't accept that when we offer it instead of their system.
Note that, right now, and since it started, the Fed "instant" check has never required the gun serial#. The only gun information used is "handgun or long gun" (because of the age requirements) and nothing more.
The current check is on the records OF THE BUYER and has NOTHING to do with the gun being purchased.
This is not what the gun control people want. They WANT a system that includes the firearm data (ser#) so that they might compile ownership list from that (no matter what other laws may say they WILL try to do that IF they have the information in the systems).
Personally I detest the idea that I may have to prove when I didn't break the law. That's not how it's supposed to work in the US.