"Move on" is about the gap between what the speaker knows and what they can actually do. They understand that the person they love doesn't feel the same way, and they accept that the sensible thing is to let go. But the opening line, "I know I must but I can't," shows how little that understanding helps.
The poem's turn comes near the end. After admitting twice that it hurts, the speaker describes living in denial, repeating to themselves that they're not affected, not sad, not hurt. The short, plain lines make these claims sound like a script they recite rather than something they believe. That's what makes the ending sad: the speaker has just told us the truth, then lists the lies they use to get by.
The mood is quiet, raw, and a little stuck. There's no dramatic outburst, only a person caught between knowing and feeling, trying to hold themselves together.