What does it really means that packet is at “proponent pending qualification”?

The Proponent looks over the packet to ensure you are actually qualified for the job before sending it to the board who will select if you are desirable as a Warrant Officer.
Just because you are qualified doesn't mean you will be selected. The Proponents also recommend approval or disapproval of waivers for the approval authority to sign off on.

I presume you’re referring to a Flight School packer. If so, the message means that the packet is being reviewed by the screening team before it goes before the Selection Board. The team checks to ensure that all mandatory requirement have been met/complied with in the packet. Items that can be waived or are preferred, but not mandatory, are also checked and verified, and noted accordingly. Anyone have other items that should be mentioned?