Because once you vote, you are seen by present and future politicians as someone whose vote can be swayed by policies that you like.
For instance, people over the retirement age vote in huge numbers, while younger people vote in lesser numbers. This leads politicians to fall all over themselves to give younger peoples’ money to older people. If turnout among younger people skyrocketed, regardless of who they voted for, politicians might decide that it might be worthwhile to oppose giving younger peoples’ money to older people to get a piece of that action and win despite the opposition of the older people. They might also try repealing the current selective alcohol prohibition targeted at younger voters, in an effort to appeal to them.
This isn’t to say that people should vote randomly or without serious reflection. And there’s always the danger that the politicians will switch to giving older peoples’ money to younger people instead. But if the politicians abandon the idea that they can screw you over to satisfy their constituents that actually vote, this is all to the good. If you have good ideas that you want to see enacted, or bad ideas that you want to see repealed, voting for the “lesser of two evils”, while frustrating, at least puts you on their radar screen and encourages aspiring new politicians to look for ways to appeal to you. Staying home just leads them to think that you don’t care and won’t resist when your money is taken and used for the benefit of voters.
Answering telephone polls might also be a good idea.