What is the biggest criticism of the electoral college system?

The biggest criticism of the electoral college is that the system is inherently oligarchic. The system is set up so that the Electorates (those who vote for the president) can be essentially anyone. This is what makes up a Representative Republic and not a Direct Democracy. In our republic, we choose who gets to vote for our president, in other words, you chose a representative. In a direct democracy, you chose for your president directly

The primary criticism comes from proponents of direct democracy. The electoral college is an all or nothing system in the majority of states. For example, if yo are one of the 14 + million republican voters in California your vote means nothing as all the electoral votes - even though 33%~ should be representing their vote, is not. All 55 electoral votes go to the democratic candidate.