One theory, as Dan Vergano wrote, is "wings are brand new features" that evolved from an insect's shell. The other is that they are modifications of legs. In truth, there are other theories and many possible ways wings may have evolved.
Deciphering evolutionary history from available evidence is science with a dose of art. Pretending only two ideas exist about how wings evolved cuts out the art; vastness of the data set limits understanding of the science. The result is a worn nub of a narrative that misses the best tale: wings were swimming organs long before they became aerial appendages.
Once I read the abstract of the article, I saw my beloved aquatic theory. The omission was in the reporting, not the science. The authors studied mayflies because their tracheal gills are a likely precursors to wings. They concluded that wings grow when regulatory genes triggering leg growth and gill growth are both expressed, affirming the theory that abdominal gills begat thoracic wings as mayflies radiated into fresh waters almost a half billion years ago.
The authors also studied bristletails, a wingless insect that is an ancestor of mayflies. If you could go back a half billion years and watch for a few hundred million, you'd see tiny silverfishy things slithering into fresher water and drier habitats, breathing through gills, then flapping gills, then flapping thoracic gills built for power, which became wings.
This is a dragonfly, an early offshoot of the mayfly lineage. Mayflies spawned all insect lineages.
