Nibbana is not destruction of self because there is no self to begin with. There is only the habitual tendency to grasp at a self. Usually one of the 5 khandhas (body, feelings, perceptions, mental formations, consciousness) is what we take to be a self or belonging to a self. When we see that all these things are impermanent then what is there that is worth grasping at or clinging to which we can safely identify as a self?
It is this grasping at a sense of self through the lack of knowledge that there is no self (and taking that which is impermanent to be permanent) which causes suffering.
Four types of letting go:
1) Giving; expecting nothing back in return
2) Throwing things away
3) Contentment; wanting to be here, not wanting to be anywhere else
4) "Teflon Mind"; having a mind which doesn't accumulate things
- Ajahn Brahm