What is the Filioque and why do Orthodox reject it?

The Orthodox view is that the Holy Spirit proceeds from the Father. The Roman Catholic view is that he proceeds from the Father and the Son. Those three words, and the Son, are what's called the Filioque. It was an addition to the Nicene Creed. It was never taught by the apostolic fathers and it was never part of the Christian faith. Why don't we believe the Holy Spirit proceeds from the Father and the Son?

We would say it contradicts scripture, and it was never taught by the church fathers. The issue comes down to the Nicene Creed itself: is that creed divinely inspired by the Holy Spirit, or is it just kind of our best guess?