No matter how he denies, In Zenitsu's heart, he still wanted to become a Demon Slayer, whether for himself or to fulfill Gramp's hope. In fact, he did not literally didnt even want to be a demon hunter till this chapter, he only denied it because he had so little self-esteem, yet he still went through with what had been put on him, Final Selection or Pillar Training.
Zenitsu may bawl his eyes out, but he is still trying his best to reach the expectation other had set up for him, especially Gramps.
Because he is Gramp's "Pride and Joy"
-AntiZenitsuHate Foundation