on what the Buddha taught
'Isn't the desire to end desire a paradox?'
Suppose you grab a log and you caught a splinter. This splinter is a sharp foreign object and it would be wise to remove it (it could lead to an infection). To remove it we could make use of a (disinfected) needle. A needle is another sharp foreign object. So, we use a sharp foreign object to remove a sharp foreign object. Do you see any paradox in there?
We don't just stick a needle in there and leave it there too, that would not be skilful. When the splinter has come out that needle is easily cleaned and put away.
Desire or attachment to the path can be compared to the holding to (and skilful making use of) the needle. Letting go of that is more about implying what will be done, instead of something that you need to focus on as 'need to do'; skilful desire leads to the ending of desire.