The thing is that employers are looking for more than just fitting requirements - they are also being influenced by subjectives (how you act, look etc) and even by pure luck. Their excuse may be that you are not qualified, but it is just as likely in my opinion that it could have been a change in market conditions, or their opinion of you as a person, or even the job description may have slightly changed during the process. You can always ask for specifics.

A long time ago I used to work in recruitment, and the two biggest things I learnt was that the requirements mean almost nothing, and that apart from entry level jobs (grad positions), how you frame your experience to what they are looking for is the most important part of applying.

I'm sorry to hear about your difficulties, but the fact you passed i) the resume screen, ii) multiple technical tests and iii) some interviews is a good sign - I would be positive and just look for another company that feels you fit better.