I voted to leave because of how EU is moving - they patently don't like Britain, and Merkel's whim of inviting 1m+ migrants to feast at the taxpayers' table was staggering.
As a 26 year old who lives at home, I followed a lot of my parents' sentiment regarding the EEA / common market, and how that morphed into an EU superstate. Whilst their musings were based on rose-tinted nostalgia (dad born 1945), lots of what they said gave me context that made me feel it appropriate we left the project rather than try to "fix from within".
As mentioned by others, I voted to leave predominantly because it was one of two options. I felt voting remain would have dire consequences for our descendants (30+ years from now), and I also felt that Britain is uniquely placed to make independence work (global connections / anglosphere etc).
If I didn't live with my parents, I would have voted remain. I would have done this for one reason - freedom of movement. I am a strong believer in qualitative immigration (not Merkel's rabble), and feel the current government will effectively pull up the drawbridge, cutting many of the options previously open to the young.
Bill Gates was quoted as saying 20% of errors affected 80% of users - fixing those errors made 4/5 of complaints go away. In my opinion, if the government made mutually beneficial qualitative immigration one - if not the - main objective of Brexit negotiations, it would quell most dissent on both sides (remain/leave).
As it stands, it feels like SS Brexit is full steam ahead to port "little Britain" where all the retirees can further lament on the "good old days", living ever harder on time borrowed from their parents, money from their children.
Such policies as 180 day visa-free recreational period for EU citizens (already enjoy 90-day), readily available work permits for EU citizens, education partnerships with Singapore & Hongkong (swapping students), anglosphere / commonwealth trade partnerships, a fund for EU citizens who wish to set up businesses in UK... would greatly lessen the blow of Brexit and hopefully spur our continental partners to similar ideals.