There is a huge difference between union and unity. Two churches can merge but that may not be unity either. That is union, not necessarily unity. If we tie two cats by the tail and throw them over a clothes line, that is union but not unity. Unity has to do with healthy relationships, not structure.
Mechanical union is phantom, a counterfeit for unity of the heart.
Paul appeals to unity on the basis of four fringe benefits every Christian enjoys at salvation. They are statements of fact. All four grounds of appeal are based on some fact that is true of the Christian. The argument is based on our divine provisions. There is encouragement in our union with Christ.