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One of the first suggestions for electing the President was a direct vote. However, it was quickly and resoundingly rejected.
The basic problem with having a popular vote was that it didn't take into account the differences in how how Southern society was organized compared to the rest of the country. In particular, slavery. In most states the only people who were allowed to vote were free male property owners. The problem there is that the society in the southern states (Virginia and parts south) was set up with a very small aristocratic land-owning elite, and nearly everyone else was a slave or worked for a plantation owner. The northern states had a lot more small family farms and businesses, and consequently far more eligible voters.
So in a flat popular vote, these Southern states would be forced into an impossible choice of either accepting almost no say in who is elected President, or of giving the power of the vote to their slaves and hirelings.
So some kind of other system was going to have to be used. Since a representational compromise had already been reached on the makeup of Congress, the easiest pull was to give each state one vote for every Congressman (Representative and Senator). The Constitutional Congress delegates knew they could pass a vote on that, because they'd just done so a few days before when they were deciding on the makeup of Congress.
Of course this previous agreement included the notorious 3/5ths Compromise, where slave states were allowed, for the purposes of increasing the size of their delegation to the House of Representatives, to count 3/5ths of their slaves, who they had no intention of ever allowing to vote.
Short answer: because slavery.