This is a really tough problem, but the past 4 presidential elections have ensured that this becomes the case.
It started with 2000, when the election was decided by the supreme court. A decision that was later shown to be wrong based on actual vote.
Then, in 2004, there was a close election between two weak candidates that was ultimately swayed by a blatant lie (Swift Boat Veterans for Truth), and rather than any repercussions happening for those who spread the lie, they were celebrated as political geniuses. Seriously, the main guy behind it has written several books and is a recurring presence in elections since then.
In 2008, the youth of the country was inspired to come out and vote in huge numbers by a charismatic candidate, promising Change. After the election, several big promises were put on the back burner, a big one was flat out cancelled (Getting rid of the Patriot act), and life went on pretty much exactly the same as it did before. Then the economy tanked. Kids get out of college with unprecedented levels of student debt to find that the jobs they hoped to get were not to be found.
The Democrats held the House, had a super-majority in the Senate, and the presidency, and they managed to change an extremely small amount of things in anyone's day to day life.
Meanwhile, gerrymandering has proven to be extremely effecting (as well as common), and there is no protection against it. Elections are bought and sold pretty much right out in the open now with PACs. Voting machines that change votes and have no paper trails.
How can you expect a generation that grew up seeing all that to have any semblance of faith in such a system? I'd love to be able to make a good argument that voting really matters and perhaps persuade some people to actually go out and do it, but looking back at my own voting history, it has never made the slightest difference. Not even on the city level. Every single person or bill that I've voted for has won or lost by such a huge majority in my neighborhood, city, county, district, or state that if you took out all my votes, plus 10% of all people who voted like me, it wouldn't influence an election. So, it's actually pretty hard to make a strong case that voting holds the power to change anything.