Apologies, I know nothing about this at all, but why is it more surprising for HIV than other viral diseases that do have successful cures (like hepatitis C)?
In simple terms, rather than always using a cell it takes over to make as many copies of itself as possible which then circulate and get dealt with by the (possibly boosted) immune system, HIV can hide itself in human DNA and let the normal human cell division process create a reservoir of apparently normal human cells which can produce copies of the virus in future
TLDR: HIV edits your genome to add itself into it.
It's called a retrovirus. There is a handful of them dangerous to humans.