Take another look at the original sentence:
You wanted to fix it this way:
A good way to fix a comma splice is to add a coordinating conjunction like but. When you use this method, however, you must choose a coordinating conjunction that logically connects the two main clauses. In the example above, but is an illogical choice because the sentence is not showing contrast.
You might want to consult the rules for fixing comma splices and fused sentences.