The anti-federalist biggest argument against ratification of the constitution was that

They did not wanted the central government to abuse their authority.

Explanation:

The initial draft of the constitution was created to ensure that the citizens of United States have the highest power within the government. The founding fathers analyze the weaknesses of monarchy system (which was the dominant system back then) and purposefully designed the constitution to fix those weaknesses by reducing the power of the central government.

But, a group called the Federalist appear and advocated for the change of the initial draft of the constitution. They believed that the initial draft make the central government became very inefficient. The anti-federalists opposed this and  believed that the initial draft of the constitution was created to balance the power of the states and central government. They fear that if they made any change/ratification to this initial draft, that balance will be disrupted.

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