Because you effectively end up with different coins right? Even if it doesn't break the on-chain connection with your new coins, it breaks the connection with your old coins?

Old coins mixed with different old coins = new coins (mixture of different origins)
Old coins mixed with same old coins = new coins (same origins as old coins)

I had thought the point of a mixer was to mix your coins with other peoples, not just your own. Surely this defeats the point of a mixer if you're just running CoinJoin with yourself?

I get that the coins would still technically be new, but it doesn't do anything to break the connection between old and new coins if you're only mixing coins from the same origin...