There is some misinformation in this thread and I'll go into more detail below. First off, in answer to your question, the result you are getting is a combination of omitting score effects, assuming Corsi is the only possession metric and poor methodology.
First of all, for what you are trying to do unblocked shot attempts (Fenwick) probably works better than all shot attempts (Corsi). This is fairly minor.
The real meat is that you are ignoring score effects as others have mentioned and this is compounded by the method you are using. The "score effect" is the tendency of teams that are behind to push harder to catch up and therefore have better possession numbers than they normally would. There are a couple ways to account for this but the best one currently available is to use score adjusted Cosi/Fenwick.
The third issue is your methodology throws away large parts of the signal you want to measure. When a good team falls behind they are more likely to out-shoot their opposition and do so by a wider margin. By using a binary win/loss for a single game you are essentially discarding all this data. Since you have thrown away so much of the signal of interest it's much easier for noise/bias like score effects to show up and skew your result.
Stepping back at bit, possession metrics like Corsi are important for a few reasons.
At the highest level Score Adjusted Coris/Fenwick are the best predictors of of future wins currently available. (It's important to remember this means it tells you who has the best chance to win not who will win. Think of it like roulette in a casino. the house has the best chance to win that doesn't mean they win every game or that some people don't walk away ahead, it only means that the odds are not in favor of them doing so.)
It's not a complete metric in that it doesn't factor in goal tending and special teams, but even without doing so it's the most predictive metric available and because they are not already factored in you can still account for these other factors. E.G the Rangers are 18th overall in 5 on 5 Score adjusted Corsi, but because they have good goaltending and special teams they are certainly much better than the 18'th best team overall, but they are still unlikely to be the best team in the NHL.
While Corsi is a proxy for puck possession it also correlates well to scoring chances. This is very useful because tracking scorning chances is very subjective. Even if they generally agree on who is getting more the numbers themselves end up different so you can't just combine the numbers generates by different people, and there are to many games to have them all done by the same person. Since Corsi correlates to scoring chances, you can use it as a proxy for who is getting more scoring chances. (Which makes sense or possession wouldn't matter)
Mathematically speaking the score in a hockey game is (Your shot attempts * their save %) - (their shot attempts * your save %)
It turns out that Corsi/Fenwick (shot attempts/unblocked shot attempts) is the most manageable part of this equation. If a team wants to improve in Corsi/Fenwick it's you can identify coaches, players, systems, play-styles, tactics, etc that improve this much more readily than you can other aspects of the game.
It's much more difficult to influence save % or shooting %. Over large enough samples the only thing that measurably impacts save % is the goalie, while the only thing that seems to measurably impact team shooting is the career shooting percentage of the players on the team. Teams with a lot of players who have had high sh% and lots of shots over their career may be able to sustain sh% higher than the NHL norm, but everyone else tends to regress to the norm. Likewise sv% tends to regress to the career sv% of the goaltenders on the team regardless of coaching, strategy, "attention to detail" or any of the other catch phrases that get thrown around.
