Voter apathy stems from just three causes. The citizen who doesn't vote either:
#1: Dislikes all presidential candidates. ("All politicians are the same."), or
#2: Feels their favorite candidate isn't going to win, irrespective of whether they vote or not. [Many who support independent candidates feel this way], or
#3: Is just too lazy to vote.
There's hope yet for those suffering from number three: they may be bored on election day and decide to vote. Most apathetic voters though fall under the first two categories.
There are reasons though that these categories don't hold water.
#1: Dislikes all candidates
People often say "It won't make a difference to my life whoever wins." That may actually be true, but it's also selfish. You need to consider your community, your countrymen and finally the rest of the world. Maybe your life is pretty well set, but what about those who aren't so comfortable? Many were given short straws in life. What effect will each presidential candidate have on the education, health and economic opportunity for such people? Two presidential candidates can affect the destinies of the downtrodden in starkly contrasting ways.
Then you need to go broader and question the footprint your country will leave on the rest of the world, based on whoever is in power. In countries like the United States and many European nations, your government has a pervasive effect on millions of lives across the globe: Different candidates have differing views on war, financial aid and sanctions.
Your vote is never just for you or your family; it's for the rest of humankind too.
#2: Feels their candidate has a remote chance of winning
If you don't support a mainstream political party, then you already know your candidate will never be president. However, such a candidate isn't running to become president; they just want enough votes to gain a seat in congress or parliament. From here they can give your views a voice and ensure you're counted. Your candidate may not be able to pass any bills or single-handedly change any law, but when the ruling party drafts any new legislature, your independent candidate will help ensure the interests that you voted for get included in the equation in some small way. There's no guarantee your independent candidate will always be heard, but their mere presence in congress or parliament is better than none at all, no?
Voting wasn't always a right
The right to vote in many countries was paid for in blood by your ancestors. Citing your democratic right to abstain as an excuse for not voting wears thin in the face of such sacrifice. To this day millions are not allowed to vote. Not voting could be seen as a sign of disrespect to our ancestors and strongly indicates we have forgotten how good we have it.
The biggest flaw of those who suffer from voter apathy is that they generalize. Bearing all that was mentioned above in mind, I hope we can agree that voting is a right that must be exercised.