I did and do bite myself, but the "do" is much less than the "did" as a child.
I am somehow hyposensitive to a lot of physical pain and "feeling as a body" and biting gave and gives my mind a sense of physical limitation.
And the other aspect is just seeing the mark of the teeth, it is a new pattern at the skin, and seeing the colour of that bit changing into more red colour.
Then I like to touch that mark with my other hand, as it felt different to the "normal" skin pattern, so that it becomes a way of a pure tacticle sensation.
In my view I do not hurt myself wth it, it is not meant to.
It does not hurt.
I can "chew" on my skin, but not in a sense of hurting myself, it is a tactile experience and a visual.
edit to add: I bite constantly the inside of my cheeks.
There I have scarf-tissue there, but that is more unvoluntarily that I do it.
I also have a "biting-tic" in my face, that I do unvolutarily.
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English is not my native language, so I will very likely do mistakes in writing or understanding. My edits are due to corrections of mistakes, which I sometimes recognize just after submitting a text.