It's only true because they believe it. Every vote counts, even if it's for a losing candidate. The parties pay attention to the vote totals, where they are winning and losing, and what issues are connecting with voters. The parties may choose to run more moderate candidates in areas that are changing, and will set their platform based on what gets people to the polls.
Even if you're going to lose, you should still show up and vote.
If you have allowed someone to convince you that your vote doesn't matter, then they have already defeated you, and you have helped them achieve their political objectives.
Democracy cannot work for you if you do not participate in it.