I know exactly why I voted Leave and, by now, so should anyone who reads these threads. I want the UK to retain its sovereignty and I fear for the future of the EU which I see as centralised, bureaucratic, undemocratic and inflexible. If it were different, I suspect the question of leaving would not have arisen.
I will keep my UK citizenship. If I would benefit from having EU citizenship as well, I would consider the costs, benefits and responsibilities. I may have this wrong and, if so, I am sure you will enlighten me but would you make a choice between either EU citizenship (whatever that is) and UK citizenship or would you have both? If it makes sense for a Remainer, why not a Leaver? Of course, if one had to swear an oath of allegiance to the EU, that would be difficult for a Leaver, at least for this one.