Definitions:

Objective - Not influenced by personal feelings or opinions in considering and representing facts.

Subjective - Based on or influenced by personal feelings, tastes, or opinions.

Evidence - The available body of facts or information indicating whether a belief or proposition is true or valid.

Objective evidence is the available body of facts or information that has been collected which are not influenced by personal feelings or opinions. Subjective evidence is the available body of facts or information that IS influenced by personal feelings, tastes, or opinions. If we are trying to determine the truth of something or some event, objective evidence obtained through scientific means which can be reproduced or verified by anyone is the ONLY method we have to determine true cause and effect relationships. Anecdotal evidence, stories, or someone’s personal beliefs or opinions does not prove something is true. In cases where there isn't enough objective scientific evidence to determine the truth of something, those questions remain unanswered until a time when more evidence can be collected which might be able to answer those questions. When you have been convinced of something and there is no objective evidence that can support that belief, then that belief is unfounded. I would not try to argue someone out of their beliefs. I don't really think that is even possible. But, I like to know that my beliefs can be supported by objective evidence. I find it difficult to understand why people are more convinced by subjective evidence (anecdotes and the like), but for a lot of people that seems to be the case.