First, please note that it is not society that should be broken into parts, according to this essay. Instead, it is the government. Madison argues that the government should be split into parts, each with the ability to check the others, so that no one part of government would be able to exercise too much power.
If the government is not split, one part of it could do whatever it wants to do. This would make that part of government much more likely to infringe on minority rights. But if the powers are divided, then more parts of government have to agree in order to oppress a minority. Madison thought it was much more likely that an undivided government would be more likely to agree to oppress a minority than a divided government would be.