The strongest argument against banning plastic bags is an argument based on freedom and individual choice. It would clearly be better for the planet if plastic bags were banned, but we also have to consider the idea that the government should not simply ban all sorts of personal choices that might harm the environment.
One of the major tenets of capitalism and democracy is freedom of choice. We try not to infringe on people's freedoms any more than is necessary. We constantly have to balance between freedom and other important goals such as environmental preservation. In this case, you could argue that banning plastic bags is a major imposition on people. It makes life less convenient for them. You could argue that there is not enough of a benefit to be gained from banning plastic bags to make it worth curtailing people's freedom of choice.
In general, democratic governments only ban things that are truly harmful to society or to individuals. You need to argue that plastic bags are not harmful enough to warrant the infringement on our right of choice.