Can you help me understand indistinguishably as described in the CPA security definition?
Yes, your intuition is completely right (assuming a polynomial-time adversary and a super-polynomial message space, which is the usual setting). If the scheme were deterministic, then the adversary could simply use the oracle to distinguish which message was encrypted. Therefore, no deterministic encryption can be CPA-secure. This is a well-known implication of the definition of CPA-security.