A simple example would be if I want to pay someone a large amount of money (>$10,000) privately. Using credit or a check creates a financial record. Cash is the only way to keep the transaction completely private. With such a large sum, it can become non-trivial to transport that much cash, especially internationally. There's also the obvious issue of securely transporting that much physical currency. With cryptocurrency, I can transport arbitrary units of value over the internet with the security of cryptography.

You may argue that there's no legitimate transaction that would occur at that high of a dollar amount, but I think that's a matter of opinion, and that individuals should be able to transact one to one without involving any third parties to transfer value.

> And how are you able to avoid taxes with bitcoin in a way that is legal?

This is a bit of a gray area. At the most illicit end, it's a total tax dodge by laundering/concealing income. At the legal end, I understand that there are cases where the taxes you're supposed to pay on bitcoin gains works out better than if you had made that gain through a stock or other type of investment. I haven't converted large amounts of cryptocurrency to USD or vice versa, so I'm not totally familiar with the IRS reporting for crypto assets.