A different take on supergirl's origin (TV version)
I know what you're thinking. You're thinking that supergirl (like superman) is a kryptonian who was sent to earth to escape the destruction of Krypton. My theory, however, is that supergirl (the TV version) is not a kryptonian, but rather an entirely new character.
So... Where does my theory begin
My theory begins with the recent connection between the Flash/Arrow universe and the Supergirl universe. Now that we know that these shows exist in the same universe, we can begin to incorporate characters from one into the other. (Please keep in mind that more character crossovers are possible because supergirl and flarrow are made by the same people.) It is my belief that the supergirl/flash crossover has a lot of meaning to it. I believe that the crossover is actually being used to connect Arrow to supergirl and the only way to do that was to use the flash.
Why connect arrow to supergirl
While there can be several reasons for connecting these shows (aside from giving everyone nerdgasms) the main reason could be something entirely unexpected.
Lian Yu Is The Source Of Her Powers!!!!!
Arrow is in middle of investigating some mystical spooky stuff. This is happening around the same time as the supergirl crossover. It may be possible that this mystical island is the source of her powers and the execs just took the first steps towards the new supergirl origin story!! While this may seem a little strange, you can't deny that the timing makes sense.