The Antifederalists did not like the new constitution that had been written at the Constitutional Convention. They felt that it took away too much power from the states. They generally preferred the way that things had been under the Articles of Confederation. Since they did not want the new document to be ratified, they would have disliked anything about the ratification process that made ratification more likely.
One major aspect of the process that made ratification more likely was the fact that not all of the states had to agree in order for the Constitution to be ratified. Under the Articles of Confederation, any major changes had to be agreed to by all of the states. This would have made it much harder to ratify the Constitution. With the process that was set up, however, only 9 states had to agree. The process, therefore, made ratification much more likely to occur. This would be a major reason why the Antifederalists would not have liked it.