You are right that this question feels more like a formal logic problem, akin to the problems we looked at in the Arguments book. Still, you can solve this problem without creating arrow diagrams or using other formal logic notation. Remember, while formal logic is not assessed directly, logic is tested extensively on the GMAT.
The way I approach problems such as this is to work through each answer choice, determining whether each conclusion is directly supported, not supported or outright contradicted by the stimulus.
A) Contradicted by the first sentence
B) Not supported by the text
C) Directly supported by first sentence (Some bad writers cannot improve)
D) Not supported by the text
E) Not supported by the text
The toughest part of the question is analyzing the answer choices that are not directly supported by the text. The best way to analyze these is to take the logical opposite of the answer (all vs. not all) and see if it is logically consistent with the stimulus.
Let's take B for example. It is possible that all writers had to be taught to be better, since great writers require skill. It is ALSO possible, however, that there exist some great writers who were able to improve their skills without the aid of a teacher. So both choice B and its logical opposite (not all great writers...) are consistent with the stimulus.
Let me know if this helped!