Just because someone is a skeptic or cynic and rejects any suggestions or answers in a debate that are absolutist in nature, does it justify not debating or not pursuing answers at all? I find that a lot of people who call themselves cynics are actually just people who are unwilling to engage in thought and are misusing that term.
I don't think you should let others should tell you which actions are justified, OP.
If you have fun debating, then debate.
I think it's impossible to not pursue answers regardless of your decisions though.
Perhaps Nietzsche should have attacked apathy rather than nihilism.