Why did the writers of the Constitution feel it was necessary to create a new plan of government?

The Framers wrote the Constitution because they were thoroughly displeased with the system of government established by the Articles of Confederation, which as the name implies was theoretically a federation of independent states. They wanted to radically change the government and thus they did not use the Articles of Confederation as a starting point. In addition, the terms of the Constitution's ratification were different than those of the Confederation: for it to come into effect, only 9 states had to ratify for the Constitution.

Since it can be argued that ultimately all the states eventually ratified the Constitution, this was apparentlly a legitimate amending of the Articles of the Confederation under the rules of the Articles. If 9-12 states approved, the Constitution would still come into effect in violation of the Articles rules forbidding any other alliance between states. One of the reasons for this is that if 9 or more states formed their own alliance, the other states would become fully independent and lose the trade and defense benefits of the Confederation, and this put additional pressure on the last ratifying states.