I'm pretty sure that before the Hakurei Border, youkai were even stronger than they were in modern Gensokyo. The border establishes at 0 AD, and before that were many many events as well, such as the war for the moon's surface.
And specifically, 1000 years ago was Yuyuko's death as a human, so that had even much more youkai occurrences oppressing the innocent.
Analyzing her further:
In MarisaA's scenario, Byakuren mentions she was sealed for using magic, and that she wanted people to call Youkai equals because
she could use magic.
She asked if it was "okay" to use magic.
And when MarisaA says that humans are still being oppressed, Byakuren denies it saying that humans haven't changed, hinting that things were always the same.
This makes me presume by using "magic", she means to kill people.
In SanaeB's scenario, Byakuren says she wants to create a world where all is equal because Youkai is oppressed, and she attacks Sanae because Sanae disagrees.
But what god me thinking is ReimuA
In ReimuA's scenario, she says "but youkais are hated and gods worshiped. That's because humans decided it should be that way".
What this means is that Byakuren believes that the equality is humans should worship Youkai. And when Reimu questions if it's okay to leave her alone, Byakuren jumps to the conclusion that she cannot change her opinion of youkai so Byakuren tries to kill Reimu.
Reimu, who was able to see her true colors, says "Yep. There we go", hinting that she had a theory Byakuren was suspicious. Meanwhile, Byakuren comments humans are selfish and self-centered, when they've done nothing at all but resist Youkai oppression. Exactly what was in this case scenario where Byakuren tries to attack Reimu, with this being irony.
I'm convinced that Zun wrote her as a psychologically ill character with distortions of a twisted reality. Again, Byakuren is a character who is ironic.
edit:
To further enforce my theory, here`s an analogy:
Zephiel is to Fire Emblem as Byakuren is to Touhou
edit#2:
And SanaeA
Sanae just wants to return home. Byakuren questions her and Sanae simply says she's a hunter of youkai who do bad things. "I see humans haven't changed" is what Byakuren says in response.
Byakuren "grieves for Youkai that are oppressed by humans" and she did says she did everything in her power to create an "equal world", but she was still sealed away.
"Gods and Buddhas are no different from Youkai. Yet why are Youkai and gods worshiped?" She also says.
When she asks Sanae if she believes Youkai hunting to be just, Sanae responds it's needed to keep the peace.
Byakuren then concludes herself no better than a Youkai and attacks Sanae.
This backs up my theory is that Byakuren wanted Youkai to be worshiped. And this backs up that the reason she was sealed away was because she attacked humans.