Why is the Electoral College considered "51 separate elections" instead of one national election?

Because each person does not actually vote for a president. When we vote for a candidate we are actually voting for a group of electors, to elect our president off of each states popular vote excluding Maine which does proportional voting.

Explanation:

Let's say you live in Kansas and electoral votes are based off of number of Congressmen/women which totals 6 2 senators and 4 reps which equals 6 electoral votes. A person voting in this state is voting either for 6 republican electors or democratic electors. When you vote for a candidate if that state goes republican those 6 GOP electors vote for the nominee that the state won. Washington D. C gets three electors even though it is not a state. So each state holds a separate elections since we all are voting for electors of the party you vote for. As well as D. C which that right was given to them in the 70s.