When any person makes a claim we have the right to ask for proof. Proof can come in many forms and what constitutes as acceptable varies from situation to situation. However, the burden of proof is always on the person(s) making the claim. If it were not this way we would open the floodgates to believing anything, no matter how absurd. This, in turn, can have dangerous results.
We could try to disprove a claim if we wanted to. If someone, for example, were to claim leprechauns exist we might cite lack of evidence or show that show that leprechauns have only ever appeared in works of fiction. However, is not up to us prove their non-existence and we can rightfully dismiss it until the claimant shows us acceptable proof.
Proving a negative
When a person says something like ‘you can’t prove leprechauns don’t exist’, they are asking you to prove a negative. This is sometimes called shifting the burden of proof. If we allow this all a person has to do is make any claim, no matter how absurd, and say it is true because the other person hasn’t or can not prove it’s not true. We have no reason to accept a claim until proof is provided and it is not the responsibility of the respondent to prove it’s non-existence. A famous example is Russell’s teapot.
Proving a negative also demands that a person be omniscient. In order to prove that something doesn’t exist we would require knowledge of all possible things at once (omniscience)
“…to know that a X does not exist would require a perfect knowledge of all things (omniscience). To attain this knowledge you would require simultaneous access to all parts of the world and beyond (omnipresence). Therefore, to be certain of the claim that X does not exist one would have to possess abilities that are non-existent.” (2)
Thus, asking a person to prove a negative rejects reason and asks the impossible. Requiring proof, especially on important matters, is just smart. For example, if you had a loved one who was hurt and I said I want to pour my magic potion on them to make them better you would want to know what is and be provided pretty solid proof it works without side effects before you allow me to try and treat your loved one with it. You certainly wouldn’t let me go ahead if I said ‘You can’;t prove this doesn’t work’. Exceptional claims like a cure for cancer or mental illness, the existence of alien life, the existence of God…etc. would require exceptional evidence and can’t be accepted simply because someone said you can’t prove they don’t work/exist…etc.