Speaking as someone in the same boat, who made the final interviews of a cadet scheme (so some indication I might be in the required mould).
The bottom line is that we all self sponsored. By doing so WE chose that we should be pilots - it was OUR decision that we're good enough/the right personality/ the right PEOPLE for the job. No-one stopped to ask the airlines if we were or not.
Not saying that any non sponsored pilot is NOT the right fit, just that everyone knows someone through their training who frankly shouldn't be allowed near a paper plane, let alone 80T of jet powered metal.
The airlines want to sponsor because they can then control who they get and ensure they fit their precise requirements, rather than just assuming that a pretty blue book is enough. This latter statement is what has happened for the last ten years. It should be enlightening that the airlines appear to be deciding that this mechanism isn't appropriate.
Sad but true. No point in getting down about it. Either pack up and walk away (as I have) or keep trying...and if you do the latter, best of luck to you.