In general, it is somewhat difficult to argue that the institution of the presidency is undemocratic. After all, the president is elected by the people and cannot simply make laws by himself. However, if you have to argue that this is an undemocratic office, the best things to point out would be:
- The president's veto power. The president can take a bill passed by the Congress and prevent it from becoming a law. This thwarts the will of the Congress, which is the body closest to the people and therefore most democratic.
- The president can issue executive orders that tell the executive branch to act in certain ways. He can, for example, order them to be slow in enforcing certain laws. Or he can act on his own (for example) to create protected areas (national monuments and such) without consulting with Congress.
- The president, as Commander-in-Chief of the Armed Forces, can send troops into combat areas without consulting Congress.
These are the things a president can do that seem least democratic.