Nobody really understand how the EU works, except for a few bureaucrats.
There are too many proxies. You vote for a local party, then you find out they go into a coalition because the parliament is huge: over 700 seats. And those parties in one coalition have very different agenda's.
Then you look deeper, and the parliament's power is very limited, and most of the power lies with the council and commission.
Both are not chosen in an election but in negotiations by the governments, which tends to mean certain countries like Germany and France have a very big say. Of course in a very indirect way these are somewhat chosen by certain part you of the people in the EU.
They've been very careful to not let the curtain slip too far, and preserve the appearance that popular opinion can change policy. But there's no legislative connection.
This kind of legislation is an interesting case in point. Who wants this? Who benefits from this? Is it actually going to make a dent in child abuse? Generally the EU is keen on privacy, so what changed that for this? Are there any states really pushing for this so they can read their citizens' mail (Poland, maybe, I guess, but they're not having a great time in the EU at the moment so probably not)? As TFA says, this is not a popular move, and there's no popular wave of anti-pedo sentiment at the moment, so why now?
The suspicion of palm-greasing (sorry, "lobbying") remains. Reading our messages means more data for the AI, means better ad targeting.
"The most up-to-date statistics (as of July 2016) show that in 2014 Poland received €17.436 billion from the EU whilst only contributing €3.526 billion. Poland also received nearly €2 billion more in EU funding than any other member state in 2013 (France being second highest). " https://en.wikipedia.org/wiki/Poland_in_the_European_Union
You are describing a representative democracy, the parent pointed out the lack of direct democracy in the process. And I would tend to agree that there needs to be more direct democracy involved at some point in the policy making process to accommodate just such a scenario where it's clear the vast majority are not happy with the result.
Representative democracy has it's place, but the reality is that you cannot pick and choose - most people want privacy, but most people are also aware of the wider issues and concerned if the fringe parties are competent enough in making decisions in other areas. Perhaps a good compromise is to be able to shoot down their propositions, so that even though they may not further the ideals the majority want in all areas, they will at least be prevented from eroding them. But as the parent pointed out, there is no mechanism in place to do this currently, so people are limited to protests and petitions.