The text says to use knowledge to remove ignorance, but then to 'throw both away.' Can you elaborate on this paradoxical teaching?

This is a profound spiritual instruction. Chapter 8 explains that both knowledge and ignorance are ultimately modifications born of nescience (avidya). The teaching uses the analogy of using one thorn to remove another thorn that is stuck in your skin. Once the first thorn is out, you do not cherish and keep the second thorn; you discard both. Similarly, you must first use the 'thorn' of knowledge to remove the 'thorn' of ignorance. However, as Chapter 8 clarifies, the ultimate goal is to transcend even this relative, conceptual knowledge and remain in the pure, unconditioned state of one's own nature, which is beyond all such modifications.