Take another look at the original sentence:
You wanted to fix it this way:
A perfectly legal move in writing is to connect two main clauses with a comma and a coordinating conjunction like but. The important thing to remember, though, is that you must choose a coordinating conjunction that logically connects the two clauses. In the example above, but, a transition that shows contrast, is illogical.
You might want to consult the rules for fixing comma splices and fused sentences.