Based on the River Sutta below, I can definitely understand assuming the self to be the body. So, when the body becomes old, diseased and approaching death, one assumes that "I am" becoming old, diseased and approaching death. If his body dies, he ceases to exist. This makes him suffer.
However, I need much better examples for the other four aggregates.
For example, if one assumes the self to be perception, it could be like she assumes the beauty of her body to be her self. "I am this beautiful woman". So, if she loses her beauty due to ageing or disease or accident, then she would suffer. Is this assuming self to be perception (about the body) or is this assuming self to be the form? Or both? Or is this mental fabrications?
Another case is let's say, there is a priest of a religion that is strongly based on the belief of God. So, this priest assumes his self to be the "God believer and servant of God". He often prays, "Oh God, may I never stray away from believing in you." Then what if one day, he discovers that God actually doesn't exist? So, does this make him suffer because he assumes his self to be his mental fabrication of "God believer and servant of God"? Is this right?
Or how about another case of a renowned surgeon who assumes his self to be the "surgeon"? If one day, he gets Parkinson's disease (while he is still young and at the peak of his practice) that causes his hands to not be steady, then he cannot practise surgery anymore. This makes him suffer. This would be assuming the self to be the mental fabrication of "surgeon". Is this right?
What about feeling? If a person loves to listen to music, then he assumes his self to be this "music lover", but if one day he loses his sense of hearing due to disease or accident, this causes him to suffer. Is this right?
Consciousness may not be be too hard to understand. If one assumes his self to be the being that continuously is aware and senses the world around him, then idea of death and non-rebirth would cause him to suffer, because he thinks this would cause him to stop being aware of his surroundings. Is this right?
But then again, assuming self to be mental fabrications can be reframed in this way: If one assumes that "I think, therefore I am", so if anything could cause him to stop thinking as he does now, like death or coma or brain injury, then he suffers from worrying about that. Is this right?
Or, perhaps, all these examples indeed fall into multiple categories simultaneously? Maybe I cannot easily isolate a case of assuming the self to be only one aggregate, and not the other?
From the River Sutta (SN 22.93):
At Savatthi. There the Blessed One said, "Monks, suppose there were a river, flowing down from the mountains, going far, its current swift, carrying everything with it, and — holding on to both banks — kasa grasses, kusa grasses, reeds, birana grasses, & trees were growing. Then a man swept away by the current would grab hold of the kasa grasses, but they would tear away, and so from that cause he would come to disaster. He would grab hold of the kusa grasses... the reeds... the birana grasses... the trees, but they would tear away, and so from that cause he would come to disaster.
"In the same way, there is the case where an uninstructed, run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in their Dhamma; who has no regard for men of integrity, is not well-versed or disciplined in their Dhamma — assumes form (the body) to be the self, or the self as possessing form, or form as in the self, or the self as in form. That form tears away from him, and so from that cause he would come to disaster. (and the same applies to the other four aggregates - feeling, perception, mental fabrications and consciousness)
The sutta goes on to say that the five aggregates are inconstant and impermanent, and should be seen with the right discernment: 'This is not mine. This is not my self. This is not what I am.' Seeing thus, the noble disciple becomes disenchanted with the five aggregates.