Bubblegum Crisis/WMG

Sylia is a boomer.
The theory is long forgotten with the series itself, but it was one of the popular theories back in the day. "Is Sylia a boomer?" can even be seen as a parallel to "Is Deckard a replicant?" in Blade Runner, given the Shout Outs to that movie.

In the first episode, Sylia gets data downloaded directly into her mind, similarly to Meison in episode 3. Sylia seems to hear Largo/Mason say her name at a distance at the end of episode 5, at which point her eyes glow red; boomers' eyes also glow red in this episode, although it's the whole eye rather than the iris and pupil. In episode 6, he says that he and she are both of the same kind.

There is, however, a flashback of Sylia as a child, and a picture.

The followup series, Bubblegum Crash, claimed that both she and Largo are "a new lifeform that is neither human nor boomer, but superior to both". However, continuity between Crisis and Crash has problems, the biggest glitch being that boomer technology is much less advanced in Crash.

The American comic book (written by Adam Empowered Warren) claims that Sylia has a nanotech-augmented brain, which Suzuki Toshimichi of Artmic has confirmed.

Tokyo 2040 actually made Mackie a boomer (or more precisely, something which is exactly like a boomer except it isn't called one). It paid further homage to this theory by having Sylia involved in the experiment that created the prototypes for all boomers in the series (including her Evil Twin).

Genom caused the Great Kanto earthquake that catapulted it into the limelight.
There wasn't much evidence for this in the series itself, beyond Genom being the kind of megacorporation to attempt this type of Xanatos Gambit. However, the A. D. Police manga begins with a man who suspects this being killed by a boomer.

This theory also ascended into canon in Tokyo 2040, with the twist that Genom did it because.

Quincy is a Virtual Ghost using boomer body doubles to pass as human.
At least twice, Quincy has reappeared shortly after a boomer double of himself was apparently assassinated. He appears too quickly to have been remote-controlling the doubles, and letting a double act on its own carries its own risks.
 * This was strongly implied in the last chapter of the A. D. Police manga, in which a boomer tells Mason that he's found out some very interesting info, which he says guarantees Quincy will not die for quite a while. Quincy then cuts in over a computer hook up and orders the boomer destroyed no matter the cost.

Bubblegum Crisis is what happened when the Gall Force timeloop collapsed
The anachronistic technologies in BGC, the Boomers, power armour and the orbital energy cannon are all reflected in Gall Force with the "alien" Paranoids and the weapons used to fight them. In Gall Force: Earth Chapter, we learn those technologies weren't invented by humans but just copied from relics discovered on the moon which survived the battle which destroyed Chaos. These technologies triggered a planet devastating war in the 22nd century because first, the power blocs couldn't decide how to share them, and then the NME cyborgs that were grown from traces of Paranoid flesh to fight in the war rebelled. Eventually this leads to the extinction of the human race, except for one ship consisting of female refugees who flee into space to recreate the Solnoid race. In Bubblegum Crisis, the same basic technologies are discovered a good century earlier with different results. The strategic nuclear arsenals which destroy the world in Gall Force Earth Chapter are instead neutralised by orbital laser cannons under U.N. control, and the Boomers are mostly used for civilian rather than military purposes.

The fact that there seems to be a reversal of cause and effect in Gall Force (in that the Solnoids are created hundreds of thousands of years after they rendered themselves extinct) suggests that time travel is involved. The fact that in Bubblegum Crisis the technologies of Gall Force are discovered a century earlier and prevent nuclear holocaust instead of triggering it suggests that some person with access to time travel is trying to prevent humanity's extinction (and the near extinction of the Boomer/Paranoid/NME) by tampering with events.

The cause for Sylia's violent mood swings is an imbalance in her brain chemistry, courtesy of her father's unethical experimentation on her as a child.
Let's face it, having a self-replicating bioengineered construct growing in your brain and then surgically removed while a child is bound to leave some side effects. (This also explains the medication that she is shown to be on as an attempt to compensate for this.)

Sylia is the daughter of Rally Cheyenne from Silent Möbius.
Those two share a rather uncanny resemblance (ok, mostly the white hair) and affinity for technology. This conveniently explains the slightly organic nature of Boomers and their shapechanging abilities if we assume that Rally's weird half-alien biology is their basis. Rally's also around the right age since she'd be about 50 in 2040 if she was alive.

BGC 2040 is a 'next generation' linked to the original 2033-34 version.
Sometime in 2035 the original Knight Sabres were all but wiped out, except for Sylia. 2040 represents her attempt to rebuild. After all her white battlesuit is remarked upon as not having been seen in several years.