So, I've had a chance to watch the endings and now I'm trying to understand the anger centered around them. This will, naturally, be my own opinion on the subject.
"Control" and "destroy" are actually great endings on their own right. Shepard has to choose between wiping out all synthetic life in the galaxy in order to defeat the Reapers or, if he thinks he's strong enough, become the new Guardian and control them. In both scenarios I can easily understand the point of the Crucible and the relays, basically it would send a galaxy-wide master signal to shut down or control the Reapers. No problems here so far.
"Synthesis" however, makes no sense. How can you "re-program" organic and synthetic beings by sending out a pulse of energy? We're talking organic-synthetic integration here, not just changing a few lines of code here and there. This is the first thing that breaks immersion.
Another thing that bothers me is the Guardian's explanation on why the Reapers exist. So, you built machines to destroy organics in order to prevent organics from building machines that would eventually (maybe) destroy organics? Oh, no, but the Guardian insists that they "preserve" organic life in Reaper form. Doubtful since the Reapers have no free will apparently.
And what evidence is there to support the Guardian's motives? Oh, the Quarian-Geth conflict... which you can solve peacefully. The rogue VI on the Moon in ME1... that turns into EDI. Sure, I can see how synthetics might turn on organics, but I can't see how they WILL turn on organics EVERY TIME. Allegedly, this has happened before.
This rather contrite explanation raises more questions. Why a 50k-year cycle? Shouldn't that number be subject to change? Suppose the Reapers culled the galaxy during Earth's 1900s. 50k years late, humanity would probably have already created synthetics and, according to the Guardian, gone to war and been wiped out long ago. Now don't restrict this to humanity, apply this to any other civilization in the galaxy, what are the odds of this happening now? Quite high. This would explain why they leave a Vanguard behind, but then cycles must be shorter and larger than 50k years.
Another question, why must the relays explode every single time? Overload? And wouldn't that wipe out life in several systems much like the Alpha Relay in Arrival?
Moving on. The Normandy. This is another thing that baffles me. Why is the Normandy flying via a relay when it's supposed to be on Earth? Is it fleeing the battlefield? Did they forget to pick up a package somewhere? The only point to the SR2 using the relays is so that it will get stranded on some forsaken planet, though the odds favour them getting stranded in space with no habitable planet in sight. So, I wouldn't mind this happening if it were explained properly, but it isn't.
Lastly, the "Stargazer" scene. What's the point of this scene? Leaving aside for a moment the fact that the kid looks like a small adult who moves like Shepard (creepy), that scene especially fills me with, if not anger then, at least, a sense of irreverence. "The Shepard" is just a story people tell in the future but nobody really remembers what he did or even if it's true, he's been reduced to a children's tale. Nice, as if we didn't have enough reason to feel depressed.
What I would have wanted to see:
1) Whatever the ending, the SR2 and your companions stay on Earth. This has nothing to do with "bunnies and rainbows," it just makes sense.
2) If Shepard dies, I want a memorial service.
3) If Shepard survives, I'd rather have a scene similar to that in ME1 with Alliance soldiers searching through the rubble, saying something like, "I've found something," fade to black, and then, "he's alive."
4) An explanation as to why the relays must blow up. I'm fine with that as long as somebody gives me a logical explanation.
5) Either explain how the relays can "distribute" synthesis throughout the galaxy or get rid of it.
EDIT: 6) Get rid of the "Stargazer" scene.
That is all. I should go.