An experienced coder who knows how Javascript works is unlikely to create problematic code even without semicolons, but it's fairly easy to imagine how errors could be introduced as a large, complex program is maintained by multiple developers, some of them potentially less experienced than the author. Like conditional braces in C, Javascript's semicolons are an optional syntax that can be used to make code more foolproof, and therefore more maintainable - though perhaps at the expense of some programmers' aesthetic preferences.
Really, though, I find most arguments about syntax aesthetics annoying, especially when people get their passions so inflamed over presentation rather than meaning that they have to risk "insulting" people. The stakes are so small. And if what you believe is so important, wouldn't it be better to convince people rather than intentionally alienate them?
People usually think there's a 1 to 1 correlation between "I like this" and "this is objectively good" and then spend a lot of time trying to logically justify their tastes. But taste doesn't really work that way - otherwise how else can you explain the popularity of Britney Spears?
I have my own tastes about how to write code in the languages I use, but I recognize that those preferences are generally just that - matters of taste - and tend not to try forcing them on others.