What is the most likely reason southerners did not support high import tariffs?

During the Civil War era, the South was against tariffs because the South's economy relied on the import of British goods.  The North supported tariffs to protect their homegrown industries.

This is an example of sectionalism in politics.  Sectionalism is the division of the country section by section -- one section or area having interests that conflict with those of other sections or regions.  In today's political climate, such differences still occur.  For instance, the US president recently announced a plan to impose heavy tariffs on steel imports.  That sort of policy was supported in areas like Pennsylvania where US steel production is centered.  But such tariffs were opposed in other sections of the country and other sectors of industry that rely on affordable steel in making their products -- such as automobiles.