One example proves something happened, not that it always happens.

A single case establishes possibility and nothing more. Someone succeeded without qualifications, someone recovered against the odds, someone was betrayed by a person like this. Each is real and each says only that this can happen, not how often. The mind treats a vivid instance as a rule because instances are memorable and frequencies are not.

When a single story is doing the work in an argument, including your own, ask how typical it is. Look for the ordinary cases rather than the striking one. The exception is worth knowing about and it is a poor basis for a decision.