It doesn't make sense. Of course it doesn't!
Azuriel has a nice post up about why the endings don't make sense and why there's no credible theory that could correct this presumed flaw. I'm a bit surprised about this reaction.
Since I was maybe 12 years old I am constantly disappointed by movies; especially Sci-Fi movies. The only consistent thing about them is that they never make sense; not just the endings but the entire movies. And the most disturbing revelation is: the more financially successful a movie is, the worse is its logical consistency.
Is that so because most humans are stupid? Well, there are a few surprisingly stupid specimen among us for sure but that's not the point. The point is that even I, even we, who see some, or even most of the inconsistencies, don't really care in the end.
Did I enjoy ME3? Yes. Did you, dear reader, enjoy ME3? Probably. If you didn't enjoy it, was the logical inconsistency the reason? With near certainty: no.
Whether you enjoy a story has almost nothing to do with its logical consistency. And it has everything to do with the short-term emotional states you are pushed through. Whether there is something that feels like a worthy climax is much more important than whether that climax makes any sense. Similar lessons apply to many things in life, by the way: computer games in general as well as your satisfaction with your job, friendships, dating, etc.
What the movie industry has already understood a very long time ago, and what creators of interactive movies, like Bioware, understand very well, too, is this: if your story doesn't make any sense then the worst thing that can happen is people ignoring this very fact and the best thing is people talking about it and thus making other people curious. In any case it is much more important that there are big explosions and a love story at the right point in time.
In MMO-terms: there are many things about which players complain. But complaining players care and players who care don't quit.