"On your left" IMO, means "please hold your line and speed so I may make a safe pass, thank you"
IF bikers happen to be side-by-side, riding erratically, or really hogging a lane that should otherwise accommodate two riders , then yes, I feel "On your left" takes on the added meaning of "Please single up or tighten up or move right for a moment so I can have room to pass you".
I was passed by a jerk last week that seemed to feel "On your left" meant "run your $4k carbon bike off the ledge and get the heck outta my way despite the fact that we're in a no passing zone and you are going the speed limit". Needless to say I didn't budge and the fool nearly ran headon into a kid while passing me in the wrong lane when it was unsafe to do so. Of course he then slowed down to 7 mph and made me pass him
So, I don't think "on your left" means you have to give up your line, and certainly not immediately, but out of courtesy you should do so if needed as soon as it is safe and practical to do so. I expect that's what you thought it meant
Edit: like others I'm more careful in my choice of words and timing with non-cyclists. I'll use things like "Bike Back", or "Passing, *pause, 1-1 thousand*, Left" (gives them time to digest passing before they hear left, at which point they've already started moving right). And I'll slow and give more warning if it's actually a situation where I need someone to yield space to me rather than just hold course since non-cyclists tend not to process/respond to "on your left" as quickly as cyclists do, even if they know what it means. I do have higher expectations of cyclists knowing my intentions, but I've learned to always expect the unexpected![]()





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