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Once again we circle back to a team that hates the Red Wings. Sure, the Nashville Predators don't have the massive hatred against them that the Avalanche do, but the Red Wings have turned out to be the team that pushes them to the breaking point (and sometimes past it).
Even a site devoted entirely to the Predators admits that the Red Wings are the team's biggest rival in the league right now.
"Again…this had happened again. Another collapse after being up by multiple goals and this time to a team that is, by far, the Nashville Predators largest rival. The Nashville Predators had just lost their NHL-leading EIGHTH game after holding a lead after the second period." The Predatorial said after an early April game against the Red Wings.
I agree that this isn't a kick butt, kill everyone rivalry that some other teams have but it looks like the Predators finally have someone that they can hate so much that it pushes them to play their best, at least until one of the teams leave the division.