It seems that their purpose is to eradicate demons. So why are they "evil", and why did Dante want to destroy them, after all?(also "assassinating" Sanctus at the beginning of the game) Is it because their plan was too crazy and not guaranteed to succeed, and might even impart danger to people living in the normal world?
"He who fights with monsters should be careful lest he thereby become a monster. And if thou gaze long into an abyss, the abyss will also gaze into thee." -- Friedrich W. Nietzsche
SPOILER ALERT (d'uh)
It is never explicitly said why Dante attacks the Order of the Sword, though there are enough puzzle pieces in the game to put it together.
It appears that the Order of the Sword's primary purpose is to defend the human population from demons. They worship the 'Legendary Dark Knight' Sparda as their patron god, since Sparda is credited with separating the demon world from the human world. (Dante, at some point, remarks on the irony of them worshipping a demon.)
Over time, the Order started researching ways to increase their might. Their lead researcher on this, Agnus, experimented heavily with demonic powers, and succeeded in infusing their elite members with demonic powers, such as Credo and some of Sanctus' bodyguards (1), and even developed an ascension ritual that allowed them to resurrect Sanctus.
Sanctus wanted to take it a step further, though: he had a demon/giant statue made (2), called the Savior, that he would use to squash demons everywhere. He needed something incredibly mighty to power it, however, and that something would need to be an open Hell Gate. If that meant scores of demons would swarm the human world, well, that was more vermin to squash, more people to save, and more power/obedience to the Order.
At some point before these events, Dante and Trish became suspicious of the Order, and Trish infiltrated it. It is not entirely clear how much they knew, but they found out enough that Dante decided to attack and kill Sanctus when he gave mass, which is where the game begins.
Note: An important subtlety to keep in mind is that neither Dante nor Trish are ever seen attacking any Order members except Sanctus (leader of the Order) and anyone attacking them. Their beef is not so much with the Order as with its leadership.
(1) As evidenced in one of the earliest/tutorial scenes, where Dante shows Nero that the knights he had defeated earlier no longer look like humans, but are actually (at least partly) demons.
(2) It is not entirely clear who in the Order knew about this, and how much they knew. Credo, for instance, was obviously aware of his transformation, but he seemed to see it as an improvement or, at the very least, a necessary evil.
As for the "evil" part of the question, well, "evil" is ill-defined. It is a moral judgement on which people might reasonably disagree.
But let's take "evil" to mean: causing harm disproportionate to good. And let's focus on the bigger picture and gloss over the individual acts (like sacrificing Kyrie and Nero to power his mecha).
Sanctus' ultimate goal is not to save humanity; it is to be worshipped as their savior. The greater the misery inflicted on the population, the greater their worship of him as their savior. Actually saving people (which he could do by not opening the gates, for starters) is secondary to that. That's assuming he will actually succeed in saving them, because...
There is no guarantee that the Savior can actually stop the flow of demons, and there's no Plan B. The Savior is big, bad, and powerful, but it's not omnipresent or all-powerful. Also, it's not invincible: Dante and Nero took it out.
In the end, Sanctus' actions cause:
- clear and direct suffering to his population;
- an attempt but no guarantee at relief from this suffering;
- no clear advantage for the population;
so that I would consider them evil in nature, for most practical approaches.
What if, after opening the hell gate, although many would die presently, all demons could indeed be wiped out once and for all? Is Sanctus's plan overly ambitious?
If Sanctus' plan were to defeat all demons and free humanity forever, rather than just take credit for coming into the fight swinging, he'd have considered:
- evacuating the population, or at least warning them;
- enlisting as much aid and power as possible (e.g. from demon hunters);
- having a Plan B for when things go wrong;
- not opening the gate. Seriously.
That said, even if he did intend to save humanity from the demons, there's no guarantee that such an act could be accomplished. It would indeed be overly ambitious.
Is it that Sanctus might become the new tyrant ruler of the world?
That sounds likely, given that he wants himself and/or the Order to gain as much power through worship as possible.
My interpretation is that the Order of the Sword was originally a force for good but under corrupt leadership went off the rails. A large number of the rank and file members of the Order are still probably good and think the Order is a force for good (Kyrie, etc.) and they are just unaware that Sanctus and other high ranking members are up to nefarious things.
The Order is probably meant to be a commentary on organized religion to some degree, which is in theory supposed to be a force for good, however often times those in leadership positions let the power they wield corrupt them.