Why is the conversion from nondeterministic PDA to deterministic PDA not possible?
There are languages accepted by nondeterministic PDAs that cannot be accepted by deterministic PDAs. Perhaps the easiest way to see this is to consider inherently ambiguous context-free languages. As context-free languages, they are accepted by some nondeterministic PDA. On the other hand, every language accepted by a deterministic PDA has an unambiguous grammar, so they cannot be accepted by any deterministic PDA.