Voting third party isn't the same as staying home. If a third party candidate gets just 5% of the vote, the party gets federal election funds in the next election. This isn't some pipe dream, third parties were crossing that threshold in the 90s. It encourages the major parties to alter their positions to avoid splitting the vote, and if they fail to do so then the third party can gain traction over the long run. Further, if you go to the polls for a third party, you are presumably also voting in down ballot races, where you have significantly more impact whether you vote third party or major party.

Staying home does nothing to combat the two party system, gives no direction to politicians as to which way they ought to move to get your vote in the future, and doesn't allow you to participate in local politics.