Why is the US not a true democracy?

Your question cannot be answered because it contains an idealist mystification. Whether the political system in the United States constitutes a "true democracy" will vary based on how one defines the phrase. At this point in world history, every government on Earth publicly proclaims itself to be democratic ("Democratic People's Republic of Korea," anyone?), despite enormous variations in protected freedoms, social equality, etc. Various political theorists and ruling parties have defined democracy in vastly different ways, and our determination of whose definition is correct will tend to depend on our own social position. There is no objectively correct definition of a "true democracy." So is the US a true democracy? Yes, if you ask most of the people in charge. No, if you're asking me. And whether the US will ever have a set of social relations that would correspond to my definition of a "true democracy" will be the result of social contestation. At any given time, a "true democracy" is what the powerful people say it is. However, political movements are quite capable of changing the way power is distributed.

If you have ever read the Constitution, you will find that the Word "democracy" never comes up anywhere in the Constitution. The Founders did this on purpose. Democracy, without safeguards, is simply majority rule, even if unconstitutional.