Hawk Moth's true identity is ...

The gist of it is that I think Gabriel wielded the Peacock and his wife the Butterfly. (The bright feathers of peacocks are only seen on males, not peahens, and it would fit in with Gabriel's career. He also has no need for the safe if he has the building for Hawkmoth, especially with that book of his) The clues pointing to Gabriel are to set him up as a red herring, both to the audience and Ladybug and Chat Noir, which would create a situation that would move the plot.
The main problem with this theory is the lack of other suspects for Hawkmoth. I suspect a twin brother like itsultrabeyza, but we've absolutely know hints of one, and I ought to know better than to assume someone's existence.
(spoilers to Gravity Falls)

There’s clues and foreshadowing that seems to be pointing to Gabriel as Hawkmoth (his safe, Jackady turning him into a butterfly), but there’s some problems with the idea of him being Hawkmoth, like the times he’d have to be in two places at once, the safe even existing if he also has the building for his butterflies.

But Gabriel is still left in an incriminating situation, with what seems to be evidence and a good motive to use them, considering his wife. Considering how many fans are certain of Hawkmoth’s identity, I imagine Ladybug and Chat Noir would easily follow the same trail.

Now, I think it was Gabriel who owned the peacock. The bright feathers of peacocks are only found on the males (peahens have a much different appearance), and it would seem to fit Gabriel’s career as a fashion designer.

Side note: I think it’s more likely the butterfly somehow passed hands from his wife to Hawkmoth (there’s not much sense in keeping a picture of your wife in a place for secrets when you have so many pictures of her elsewhere unless she’s somehow related to the secret), but it’s also possible it was someone else entirely, or Master Fu just guessed wrong about Hawkmoth’s intentions. I guess we’ll just have to wait.

So my current guess for how a scenario like this would go: Ladybug and Chat Noir are trying to figure out Hawkmoth’s identity (I think this would occur after they discover each others’ identities-It would get the idea of their double lives in their heads and make searching easier, as well as allow Ladybug to know what support she would have to give Chat as they tried to confront him) and come across the idea of Gabriel for whatever reason, and plan to confront him while transformed. However, their plan (intentionally or not) occurs during an Akuma attack. There’s a bit of doubt, but they decide to power through it because if they can stop Hawkmoth entirely, the Akuma will be the last one.

Gabriel isn’t very convincing, and his one bit of solid proof actually makes the situation worse-He goes for his Miraculous to bring out his kwamii to help out, but Ladybug and Chat Noir mistake this as him trying to get powers to use against them, and think the peacock is a fallen hero he’s already stolen the Miraculous from.

Meanwhile, Hawkmoth’s gotten a bit of an edge without anyone stopping him. So here, it could take a positive route, with Fu trying to find owners for the last three Miraculouses, or a negative one, with the Akuma snagging one of the Miraculouses in the midst of their argument or somehow stumbling across the box. Either way, I think this would definitely be a situation that would move the plot along in ways it’s expected to go. (We can’t not have these questions answered, right?)