That thing must be present in any cases of that disease
and That thing must be living
The only way to prove is culturalble, because all culturable things are living
here have some problems, not all living things are culturable in limited technique. ex. some bacteria, viruses are impossible to culture under current laboratory techniques
and viruses may not even living under some perspectives
That thing must can cause another that disease in a healthy individual
key of prove
and the same thing must be isolated again from that individual
another biggest problem
That thing not have to be the only one: identity
That is true for many diseases, not only one pathogen is present