I'm honestly not sure why Pink Diamond would've cared about earth though. She'd been doing kindergartens for who knows how long on who knows how many planets, why earth? Why would this one planet in particular make a Diamond of all gems want to rebel? Diamonds have been shown to be callous and elitist and have a general "I don't care, make it happen or you'll be executed" attitude reminiscent of early english kings. Why would a Diamond give a crap about earth out of all other planets, or it's people?

You do bring up a good point. I hadn't thought about it. My best guess is because she herself saw the effects of the kindergartens on earth. I think that most planets in the Gempire were previously lifeless and that kindergartens didn't affect the planet as much as it would have affected earth. She also didn't switch sides until sometime near the middle of the war. I also believe she had an internal struggle about whether or not to join the Rebellion, showing that she at least had a conscience

Earth also seems to have an odd effect on gems in general. BD wouldn't have gotten it, since she was up in her Arena instead of actually on earth, but PD was probably down on the earth with the kindergartens. Maybe that's why?

She's similar to Peridot; they both know that the life on Earth was worth protecting

I believe Pink Diamond has something to do with the Rebellion, especially because the Authority erased her from their history, as if she has done something so shameful that future generations should completely forget about her existence.

Homeworld was a shared Monarchy, where each Diamond could possibly command a key aspect of Gem society, reflecting their views or beliefs, all for the good of Homeworld. I don't think the four Diamonds had the exact same way of thinking, but they were supposed to respect each other's independence, based of the common goal of the Authority. 

This is implied by the way Blue and Yellow Diamond possibly see fusion between different gems - while Blue is very conservative, abominating every aspect of this type of fusion, especially when it involves a member of the aristocracy and a commoner, Yellow seems to be more "flexible", as she doesn't care if thousands of different Gems fuse to form a Geoweapon - it's a very powerful weapon anyways, and that's all she needed to take over after the war and lead the armed forces all by herself. Blue might have seen this as the most gruesome of the aberrations, but had to accept.

So what about Pink Diamond? Her possible experience on Earth (as the one in command of the Kindergartens, according to a theory) changed her views, which inflicted on the progress of Homeworld as an exapanding empire (thus, breaking the presumed "balance"), causing the other DIamonds to go against her.

I figured out the timeline before the show.

• The Diamonds, leaders of Homeworld discover the Earth and decide it would be a great place to build a colony.

• Rose Quartz finds out what the diamonds are planning and hates it, so she talks to her diamond, Pink Diamond about it.

• At first, Pink Diamond does not agree, when the diamonds arrive on earth, Pink Diamond realizes the earth should be a place that both humans and gems could inhabit, She agrees with Rose Quartz.

• Pink Diamond tries to convince the other diamonds to still let the humans live on earth, the diamonds refuse and show their true colors. Pink Diamond realizes that the diamonds are really evil cruel beings who only care about themselves. She also realizes that her fellow diamonds must be stopped. She pretends to agree with the other diamonds and they don't realize that Pink Diamond is planning a rebellion against them.

• Pink Diamond sends Rose Quartz to convince White Diamond's Pearl (Our Pearl) to join them. Pink Diamond had a feeling that the would be able to convince our pearl because of her personality.

• Pink Diamond, Rose Quartz, Pink Pearl, and Pearl started a rebellion against the diamonds. The diamonds had no idea pink diamond was leading the rebellion.

• The diamonds eventually figured out that Pink Diamond was leading the Rebellion.

• At one of the battles,

Yellow diamond(the most cruel and ruthless diamond) battled Pink diamond. Pink Diamond stood up to the diamonds by insulting them to their faces. Pink Diamond stood up for what she and Rose Quartz believed in. Yellow diamond was about to kill rose quartz and Pearl, Pink Diamond got in the way and was killed by Yellow diamond.

YELLOW DIAMOND KILLED PINK DIAMOND.

What if Pink Diamond was in fact captured by an opposite fraction?

In my theory, Pink Diamond was corrupted before the gems got to earth, when they were travelling to the earth, per say, and until the diamonds found a way to fix her, Rose, one of PD's most loyal quartzes, replaced her temporairly, and for Rose to be different from the other diamonds, she resolved to change her appearence, changed her hair from spikey to curly and her outfit from battle outfit to dress, but when they got to earth, Rose noticed the harm that the gems were doing to the planet, and she resolved to rebel, since Pink Diamond's gems didn't truly trust Rose, they didn't agree, except for Rose's Pearl. In the end, Pink Diamond stayed in the earth, corrupted, hopeless and alone, I believe we have not seen her yet.

I really don't think Rose is Pink Diamond, since Quartz's aren't meant to be leaders before Rose rebelled, but that is, in my mind, the only explanation for why the Pink Diamond was removed from the insignia after the Rebellion. So this theory actually makes a little bit of sense to me. 

But that isn't real art. The Gem was replaced with Rose, so this image has literally nothing at all to do with the real plot. That unknown Gem, as far as we're concerned, doesn't exist.