This would not seem to correspond with your "good neighborhood" concept, but a very simple way this could have happened is like this...
A person standing on the cover, about 2' in from the side of the pool (this is along the long edge of the pool, not the leading bar/short end), takes a utility or other kind of knife. They first make two unsuccessful attempts to cut the fabric by drawing the knife towards them between their legs. Both resulting in the "scratches" to the side of the eventual cuts. Those attempts don't work because not enough strength is put behind the stabbing, and the fact that the cover is very thick/strong. Then the person says, "I'm gonna get through it this time". They stab downward, aiming for the ventilation hole as a starting point, though they miss it slightly. They go in with enough force to create the first cut on the left. Then they create the second cut on the right. Then they connect the two with a sideways strike of the knife at the cover. Where the lines extend beyond where the cover is actually ripped are where the knife was exiting the cover as the knife was drawn towards the suspect and the natural arc of the movement slowing caused the knife to rise.
Then they were either spooked, got tired of the destruction, had a change of heart, had retrieved whatever they were after in the pool, or whatever other motive they had was now gone, and then they left the scene. Unfortunately, they didn't leave a sorry or explanation note. Thinking that bad things don't happen in our neighborhood is something that many of us probably do. The suspect could have been a drunk person, a person you cut off on the way home, a thug, a local knife enthusiast (it could have been anyone after all).
Not trying to be funny, but rather suggest how it could have happened. Regardless of how unlikely. It's actually very plausible, it's the motive/perpetrator side of the equation that is unanswered in my analysis.
This thread haunts me due to the unknown.
- - - Updated - - -
It's definitely a difficult one to figure out. Something cut into the cover but there's no obvious answer as to what it was.
Or someONE with a something.