You don't understand how our voting system works. Why do you limit it to swing states? According to your logic there is not one state where an individual vote mattered in any presidential election. Show me one state? So why vote if your individual vote has not and will not ever matter in a presidential election?

In swing states, individual votes do matter.

It's all about statistics.

Let's say average eligible voter turnout is 50%. And let's say that a state has a 10 percentage point (out of actual casted votes) one way. For simplification purposes lets assume there are 200 eligible voters in the state. 50% turnout with a 10 percentage point margin between the two parties would mean that one party gets 55 votes while the other gets 45 votes. Now let's assume another 20 people decide they are going to vote, in order for the party that got only 45 votes out of the 100 original voters (the regular turnout) to sway the outcome the other way, it would require 16 out of the extra 20 people to vote for the party that got the first 45 votes. Is it possible? Yes. What is the probability - I'm not an expert, but I would guess close to nil. Remember, this is about having the people that wouldn't otherwise show up to vote, to be very heavily tilted the other way (in our example that would mean a 60 percentage point margin versus a 10 percentage point margin going the other way for the self-motivated voters).

Now we use the same basic numbers - 200 voters with 50% regular turnout, and the numbers are 51 to 49, then with 20 additional voters the results out of those 20 would only need to be 12 to 8 going the other way. Still a stretch, but not as implausible as the first example. The closer the margin the more each additional vote might have an effect. Wherever the margin is significant, no single additional vote counts.

That was my non-scientific explanation. But here's a more scientific paper:

http://www.stat.columbia.edu/~gelman/research/published/probdecisive2.pdf and the following image is the important executive summary (the probability of a single vote swaying the election in any of the states colored black is close to ZERO):