Prove it. Use documents such as the Constitution c. 1860 and the Federalist papers. That way I can prove the professor wrong with facts. Could be fun.
OK, start with the fact that none of the Federalist Papers support the idea of unilateral secession. Madison in his writings dismissed the idea of secession without the consent of the states as ridiculous. And as for the Constitution, states cannot join without the consent of the other states as expressed through a vote in Congress. Once allowed in they cannot combine with other states, split into two or more states, or change their border by a fraction of an inch without the consent of the other states as expressed through a vote in Congress. Clearly state cannot join or take any action which impacts the interests of the other states without approval from Congress. Why should leaving be any different, and by implication it is not.
Now your turn. Please quote the Federalist Paper that clearly says states may leave unilaterally. Point to the clause in the Constitution that allows a state to take any action that can negatively impact their neighboring states without first needing Congressional approval. Could be fun.