The hapless lover John just won't take no for an answer. He appears singularly obsessed with cultivating a relationship with the speaker and simply will not be deterred. But the object of his affections isn't for turning. She doesn't want a romantic relationship with John; she doesn't love him, and has never loved him; not now, not ever, and that's an end of it.
John is evidently hurt by his rejection and lets the speaker know just what he thinks about her. He accuses her of having no heart, of being false. But the speaker's not about to let herself be subjected to emotional blackmail. She hits back, reminding John that she never said that she loved him. Her friendship is there if he wants it, but that's about it.
John may well be feeling hurt by the speaker's rejection, but the speaker suggests that that's his fault, not hers. He may be right in saying she has no heart, but if that's the case then how can he get so worked up about her not giving him something she hasn't got? John can't have it both ways; he can't insist on winning the speaker's heart if she doesn't have one.
In traditional love poetry, unrequited love is often presented as a deeply painful experience for male lovers. And the blame for this pain is laid squarely at the door of women, who are often accused in such poems of being cruel and indifferent. Yet in "No Thank You, John" Rossetti subverts the misogynist conventions of love poetry by insisting that it is the persistent, stubborn behavior of men towards women who aren't remotely interested in them, amounting almost to bullying in some cases, that is really responsible for their intense emotional pain.