You can still write a paper which exposes an unsound or impoverished idea. Imagine the consequences of not removing an unsound or impoverished idea from your life. This first stage of intense and uninhibited exploration has some of the passion, exhilaration and despair of romantic love. The next stage requires the precision, organization and honest testing that transforms romantic love into committed loving. So, begin to put the parts of your writing-thinking into logical sequences.
Ideas have a structure and function like a bicycle.
Some ideas are illogical because they are a non-working assembly of a car tire, lamp shade, some bicycle parts and other assorted junk that pretends to be a bicycle. Some ideas are the right parts but illogical because, for example, the chain is not connected to the sprocket so that the bicycle cannot move. Your understanding of fallacies will be of use to check of illogicalness. At this point you can use the characteristics of critical thinking to provide a structure for your paper. Refine your statement of your basic issue.