To love Democracy is to love that faceless, 4th branch of government which is its most powerful - the will of the people. Divestment offers a direct, peaceable means to bend governments and corporations to that will.
Divesting from unethical institutions - and investing in ethical ones - is a surer path to democracy than even representative, indirect government, as divestment is direct action.
Divestment is widely credited with forcing the dissolution of the racist Apartheid system in South Africa. Boycotts, another form of direct consumer action, have been successful the wold over in effecting positive change.