I think your op is a bit goady but I will answer your question because I am fed up of seeing threads where leavers have been asked to explain their reasons to help those of us who voted remain understand and I have yet to see any real responses. I hope this will precipitate a fair exchange of opinions.
I voted remain. Like pretty much everyone on this thread I know there are huge issues with the EU as it is and that change /reform is needed.
However, it was an easy decision. Like people have said before me in or out we will be affected by the euro zone and if we are in we have some chance of influencing that change out we have none.
Good things about membership:
Benefit to the economy, more power to negotiate better deals as a trading block than out (maybe it takes more time as there are a lot of countries to agree but it needs to be fair to all and I am thinking long term for my children's future).
The environment (already the impact of the damage we are doing is showing I am terrified about what I am leaving behind for my children, the EU have been a positive force for change here).
Freedom of movement (we live in the EU, yes I am sure people with the right qualifications will still be able to go however without FOM spouses are left with no right to work / continue their own carers etc I see this all the time where I live as there are a number of families from the US).
My children. Why would I vote to limit their future opportunities?
EU funding for science, education and regeneration ( I used to work in regeneration - the eu don't sit in a room somewhere saying ah town x is deprived we should build a sports centre! Local government and charities apply to the EU for funding to spend in their areas, they create the project and bid for the money. if people have a problem with where money is going then the problem lies much closer to home).
Finally rise of the right wing: I am not sure why people think that the right wing in Europe is any different to the right wing in the UK? The union jack has become a symbol of right wing facism in Europe since the referendum. The right wing is on the side of the brexiteers. We are heroes to the right wing - not something to feel proud of. In contrast my little french village ran an international festival just last week to celebrate our international community. You can learn 4 different languages for €40 for the year at my village hall. Classes run by volunteers who came here like me as economic migrants and have been made to feel welcome and valued. Not quite the image projected by the DM and DE I think.
Sorry for the essay, this is as short as I could get it.