I see this all the time and nobody has given me a satisfying explanation: No shit, it's a representative democracy. You can vote for parliament members. They appoint people like the President of the EU Commission.
Your prime minister is literally appointed by your Queen. Please explain to me the difference. You didn't directly vote for May either.
This is grossly disingenuous. The Prime Minister being appointed by the Monarch is a mere formality, and the Monarch has not appointed anyone other than the leader of the party with the support of the Commons in nearly a hundred and fifty years.
The EU's structure is much less democratic than that of the United Kingdom. Here's the United Kingdom's structure:
Voters directly elect the Parliament (the Legislature).
Voters elect Parliament, who elect the the Government (the Executive).
That's it.
Here's the EU's:
Voters elect National Governments who appoint National Ministers (one half of the Legislature)
Voters elect the European Parliament (the other half of the Legislature)
Voters elect National Governments who appoint National Ministers who appoint Commissioners (the Executive)
The chain is very clearly less direct. That's not even mentioning two more complicating points: firstly, that Commissioners are supposed to act independently of the Ministers who appoint them, so in fact Commissioners are not accountable to National Governments, and are ultimately not accountable to voters. This is particularly true given that functionally the European Parliament has fuck all influence over Commissioners. Secondly, that the European Union has a legislature which has functionally no power whatsoever to legislate.
I'm in favour of the European Union and Remain, but I can also quite clearly see that the EU's structure is a mess and could do with reform.