But what about people that always have their brake lights on?
Some people do this, and they give left-foot brakers a bad name. There is absolutely no reason to ever rest your foot on either pedal. Keeping your foot poised above the pedal involves a process known as dorsiflexion, and if you're not used to it, your foot will get tired at first. This is why you see people driving down the road with their brake lights on -- it's simply someone who isn't used to it, and they're tired.
This applies to both feet, though, and if you're first starting out with your left-foot braking, you do need to be cognizant of what your right foot is doing, lest you have it pressed on the accelerator.
Even if you accidentally hit both pedals at the same time, you're still going to brake
By far the most common argument against left-foot braking stems from the fear of hitting both pedals at the same time. I spent hours trying to find data that supports this, specifically so I would have an answer for you. The truth is I couldn't find any supporting evidence that people actually hit both pedals. Even if I did find some, it wouldn't change the argument, because on newer cars mashing down on both pedals at the same time automatically cancels out the accelerator.