Lyman talks about intemperance as something that is to be fought off. It mentions it as something terrible that ruins families and that we should execrate just as we execrate the cruelties of slave trade. It isn't really a comparison. It more of an appeal to see one as a horrible thing just like we see the other.
In his own words:
"We execrate the cruelties of the slave trade—the husband torn from the bosom of his wife—the son from his father—brothers and sisters separated forever—whole families in a moment ruined! But are there no similar enormities to be witnessed in the United States? None indeed perpetrated by the bayonet—but many, very many, perpetrated by intemperance."