This question came up in the Online 10-day Retreat Nov 3, 2020, guided by Delson Armstrong. Day 6 was part of a daily 30-minute discussion on the suttas, the Dhamma talk and reflections.
They are still identifying with the process of coming out of Cessation. There's still identification going on, the fetter of conceit is still there.
One thing I want to make clear is to not equate Cessation of Perception and Feeling and Nibbāna as one and the same.  It's the experience of coming out of Cessation of Perception and Feeling, seeing the links of Dependent Origination as they arise without any involvement, and then making contact with the Nibbāna element.
At the level of contact with the Nibbāna element, there is some sense of relief that arises. That relief is the feeling that one experiences, or that is experienced by the mind.
The anāgāmi does not crave for that feeling. They don't expect that feeling to continue to be there, but at the same time they identify with the Dhamma, they still identify with the process, and there is still that conceit in them where they have this sense of I have attained this or I have experienced this. The gateway into arahantship is that there is complete detachment with the whole  process, when it arises again after Cessation of Perception and Feeling and you see the links. There is complete non-involvement in any of the arising of the links and when the mind contacts the Nibbāna element, at that point it is just seen as an impersonal and impermanent process, and not worth holding on to. So, even that relief is not held onto. And because there is no identification and holding on to that relief, the fetters associated with identification, particularly conceit - upon which the fetters of restlessness, the craving for being and the craving for non-being are based – and Ignorance are destroyed once and for all. Because now you fully understand the four Noble Truths and no longer identify with anything and there is the understanding that any identification process leads to suffering. Therefore, the mind is no longer prone to do that.