Here's an attempt at a rationalisation of voting for the individual:
1 If you choose not to vote once, you are significantly more likely to choose not to vote again. After all, you're unusual if you're in a western democracy and you are not at all disillusioned with politics and have nothing more enjoyable to do on polling day with your time.
Summary: Not voting leads to greater not voting in the future.
2 People tend to rationalise and defend their behaviour, so if you choose to not vote regularly, you are likely over time to come to believe that this is a good decision and become an advocate of not voting.
Summary: Habitual non-voting leads to advocating non-voting.
3 People are social creatures and much more heavily influenced by the norms of their peers and neighbours than they like to think. If you don't vote and advocate non-voting you are likely to strongly influence those you interact with, and most strongly affect those who normally share your opinions.
Summary: Your non-voting actions and views spread to people, and most strongly to people like you.
4 Politicians publicly advocate policies that are likely to garner large numbers of votes. If a group (eg people under 30 in the UK) vote significantly less often, parties use the money available to favour groups that vote in larger numbers (retired people vote in much greater numbers in the UK). There is thus a genuine but small risk that if your non-voting ideas spread amongst like-minded people, government policies will eventually disfavour people like you. The risk of non-minor future harm can be weighed against present inconvenience of voting. If the like-minded group we're discussing is thoughtful people, that could be quite devastating.
Summary: It's not worth risking disenfranchising the people with whom you have the most in common.
Humans are social and you don't act in isolation - you will influence people like you not to vote, and as a group you will become more disenfranchised. As an individual you can work towards or against group disenfranchisement, but are very unlikely to be neutral. Group disenfranchisement could lead to significant negative consequences for you as an individual.
That's not at all watertight, and the effects may be too slow to affect you in your lifetime. This sort of reasoning is much stronger to argue that you should attempt to befriend newspaper editors.
Rationality explains very little of human behaviour anyway. (I vote regularly, but not for any of these reasons.)
Nevertheless, this was an interesting question and a good challenge.