They would use genetically enhanced falcons, and no, they wouldn't be pushing the planes, they'd be pulling them.
Hmm... It would be interesting to do a cost-benefit analysis of raising flocks of genetically engineered birds to pull airliners.
Lets take a look, shall we? Having to make progressively better planes, or having genetically engineered birds that are trained to fly to destinations.
Plane
Costs: Having to re engineer planes and thus spending millions of dollars in production and research in new materials and systems.
Benefits: Over the short term it won't cost as much and you would not have to build storage space for their homes and upkeep. You also would not have to pay to find a substance for them.
Plane+Birds
Costs: Upfront it would cost a great deal to find a adequate substance to give the birds the drive to help pull your plane. Also upkeep of the birds and such.
Benefits: Over the long run you would save money as the birds would evolve to fly faster and faster so they can recieve what they crave at their destination quicker. There would be no need to re engineer planes as evolution would make your planes move faster. In fact, they birds would most likely grow stronger as well meaning you could make the planes lighter saving more money.