How is it hard to prove a negative?

"You were the one who robbed the bank"
"No, I was in xyz place and time playing with my toy turtle in the bath on my own, with no witnesses during the robbery."

"You're behind a mass conspiracy."
"No. I haven't any connections but with a few powerless friends. Of course it's hard to prove a lack of connections, and easy to conceal them and claim I don't have them. Meh, what can you do?"

"You're the owner of tradesatoshi and tradeogre.`
"No. I'm not Mr. Johnny Depp or ms. Jane wright. Honest. I'm sure you believe me. I take my privacy seriously enough that I won't provide a random stranger on the internet with my passport details to prove it. And why should I anyway? The onus is on him to prove wrongdoing, not make a wild claim and put me to the inconvenience. I'm pretty sure the principle 'Innocent until proven guilty' is there for a reason."