My flight was cancelled due to non technical reasons (allegedly air traffic congestion) so my compensation was denied. I suspect they are just trying to avoid paying the compensation by declaring a non technical problem (in EU passengers are entitled a compensation if the aircraft doesn't depart due to a technical fault, as noncritical it may be). Is there any reliable source out there where I can find out the real reason for a cancelled flight and use it as a proof?
Unfortunately, there is no definitive list of the reasons for delay of every flight. As you mentioned, the airline probably won't give out any information to avoid the possibility of paying the compensation.
You might be able to find out some supplemental information from a third party, though. By using FlightAware or one of several similar flight tracking websites, you could find out whether the aircraft held in the air somewhere, whether inbound flights on that aircraft had previously been delayed, causing a cascade, or if the airplane had just been sitting in the departure airport for some time. This might be helpful in your factual understanding of the issue, but might not be so great at explaining why an event (like a hold or an inbound delay) took place. (Note that this only works if the delay was fairly recent, as you tend to have to pay for information older than 30 or 60 days.)
Otherwise, your best bets to get the compensation probably are either to
- Try to sell the claim to a company like Claim Compass as mentioned in the comments to your post
- Submit a formal complaint to the regulator in the country where the delay took place. The EU has a form for this, but the process will almost certainly take a long time, even if it is resolved in your favor.
That said, unless you have a specific reason to doubt that the delay was caused by a non-technical problem, since ATC delays are pretty common in Europe, your chances of getting compensation are not that great.
TLDR: You might be able to get some information from FlightAware or similar, but convincing the airline or a regulator is going to be complex and time consuming.