There are two main ways to argue that democracy is the best form of government for all people.
First, we can argue this on the basis of universal rights. We can say that all people have the right to the sort of freedom that democracy provides. We can say, as Jefferson did in the Declaration of Independence, that government can only be just if the people consent to it.
Second, we can argue that democracy is more likely to lead to good results than any other form of government. We can say that autocrats are much more likely to get it wrong because they are individuals. The whole population is more likely to, cumulatively, make good decisions about what government should do.