What reason and evidence does the excerpt use to
support its argument that the court had ruled incorrectly
in the Brown case?
The original Constitution does not mention education
Neither does the 14th Amendment nor any other
amendment. The debates preceding the submission of the
14th Amendment clearly show that there was no intent
that it should affect the system of education maintained
by the States...
We reaffirm our reliance on the Constitution as the
fundamental law of the land.
We decry the Supreme Court's encroachment on the
rights reserved to the States and to the people, contrary
to established law, and to the Constitution
-Southern Manifesto (1956)
0 The Constitution does not discuss education, so it
should be left to the states,
The 14th Amendment prohibits the court from ruling
on matters of education,
The 14th Amendment prohibits the court from ruling
on matters better left to states,
1 There was no intent for education to be unequal, so
the court ruled incorrectly.

This started the process ending segregation. It overturned Plessy v Ferguson. PvF states "separate but equal" but we all know that did not happen. There was no fair and equal treatment to the people or to the building they went to school in. In 1954, the Supreme Court finally was unanimous with the decision that segregation must end.

Explanation:

The key here is that the outcome of the PvF was not followed through with and was was unfair. No good can come from the oppression of a people.