Obvious counter-example, which Mill addresses: some people renounce happiness (I-15).
Mill’s reply: true, but usually for the sake of bringing about happiness for others, so in one way they do desire happiness (though not their own.)
Problem with the reply: the objection stands, because it targets the claim that everyone desires happiness for himself. Mill, though, could say that the overwhelming majority of people, under normal circumstances (other than when immense self-sacrifice is called for e.g. during war) want to be happy, and that is enough evidence for the claim that happiness is desirable. So let’s accept that.
