Kennedy, who won the inaugural Brett Kirk medal, awarded to best on ground in the rivalry clashes, can't come to terms with Greater Western Sydney coach Kevin Sheedy's latest brainchild.
Joining several players from both sides in front of Sydney's Anzac Bridge to promote their opening-round clash, Kennedy said it was an insult to pigeonhole the Swans as an eastern suburbs club.
"We don't really subscribe to it (the Battle of the Bridge), nor understand it. We're the Sydney Swans and we have been for 30 years," Kennedy said.
"We're not the East Sydney Swans. They can be Greater Western Sydney, but we've been part of Sydney for a long, long time.
"We've worked extremely hard to gain the support of so many fans here, so many loyal fans ... and we'll continue to fight for our supporters up here and we know that they'll be loyal to us."
Kennedy was blunt when asked if it was an insult to categorise the reigning premiers as representing only the east of the city.
"Absolutely. When we came up here 30 years ago, we weren't given some of the grants they've been given to try and make their mark in GWS," he said.
"Our fans are all over Sydney. That's eastern suburbs, western suburbs, south, north. They're all proudly Sydney.
"No doubt Sheeds has come up with this idea. But Anzac Bridge is very much Sydney, every bridge here is Sydney - as we are," he added while speaking in front of the Anzac and Sydney Harbour bridges.
Kennedy, who polled 19 Brownlow votes last season, said he didn't expect any annoyance over the marketing of the game to spill over onto the field.
With GWS having beaten the Swans for the first time, in this pre-season, Kennedy said his teammates wouldn't be taking the Giants lightly.
"We'll go into round one like we do every game, expecting to win.
"We have a huge amount of respect for the way GWS go about their football. They've really shown they've improved, so it should be a really good contest.
"Hopefully we can start off the season well."
