Even worse (well, maybe similar, but more surprising): imagine if on Feb 28, you parse "Feb 29-Mar 1"... both of those dates could land in an entirely different year than "Feb 28-Mar 1" would, depending on whether the current year is a leap year...
I dare say I have not yet seen a single parser in my life that handles such issues. In fact I don't think I've seen a parser that can parse a date interval, or that can even do "parse this string assuming it is after that date", or anything like that.
And all of these problems are before we even consider time zones, leap seconds, daylight savings, syntactic ambiguities, etc... not just how they affect individual dates, but also ordered dates (/intervals) like above...