why did the Anti-federalists oppose the constitution

I dont know

The Federalists opposed a strong central government, and they believed that the government through the Constitution would have too much power in contrast with the States, who would have very little.

You also have to remember that the Bill of Rights hadn't yet been written, and the citizens were not about to lose the freedom they'd so recently gained in the War of Independence to a national government that would take those new found rights away.