Most Western countries that practiced slavery abolished it without a civil war. The United States is a unique case, where the American Civil War is borne out of the conflict between the landowning slaver class that had been the predominant faction of the wealthy/rich population through the country's existence up until that point, and the new industrial classes (capitalist and worker alike) that opposed slavery both for moral reasons and financial reasons. Elsewhere in the West the landowners used serfdom, not chattle slavery, but this too largely fell in time as national governments centralized their authority and needed more free manpower for their armies. Slavery abolition is entirely possible by reform, but it largely revolves around transforming the nation's economy to end dependence on it as a source of labor.
To your point about the United States being a more-or-less unique case due to its practice of chattel slavery - we also have no idea whether the setting in-story is the same, or more like the serfdom/"spoils of war" model seen elsewhere in history.
That's not to defend the practice. And, I also recall that Weiss (or at least the protagonist who becomes Weiss) isn't "for slavery" - but that his whole gripe about the confrontation with Allen was over Allen's idealism clashing with the logistical realities of actually removing a foundational pillar of a country's social & economic apparatus.
That's what this chapter is ultimately about, I think. That he's just pissed off over Allen jumping up and making these claims that, while true in essence and certainly lovely-sounding platitudes, he's doing it in a setting full of the people whose families are the
exact sort of individuals and groups who directly benefit from the practice, and comprise the social caste Allen is raving against.
Allen, and orphan commoner, is understandably passionate about the issue - but speaking out as a near-lone dissenter just causes problems for him, and for anyone close to him, and he's also offering nothing in the way of actually addressing and fixing the issue, colossal and immensely complex as it is.
And when the protagonist calls him out on that, Allen just gets pissy and verbally accosts him, and
that awakens the Actual Weiss inside him, who bares
his fangs at Allen because of the weirdly fundamental animosity between them as a part of the world's settings, or something, and
that is likely very tiring or at least annoying for the protagonist to deal with.
So yes - the slavery thing is the backdrop to the conflict of the chapter, but it's more about the protagonist having trouble keeping a lid on the asshole inside him, because Allen's blind idealism risks friction within the social fabric of the academy (which will have knock-on effects for everyone there including the protagonist the more it goes on), and is directly and personally riling up the Weiss of the setting, which is
directly problematic for the protagonist.