Please explain to me how anyone legally issues "alternative currency" when only the Government is authorized to print money.
The government isn't the only entity authorized to print money, at least not under the Constitution. The federal government is authorized to issue money, and the states are prohibited from making anything other than gold and silver money (this, btw, was intended to fix a fairly limited, specific problem; it wasn't just a general proposition uttered in the abstract), but the Constitution doesn't restrict that power to the federal government alone.
More generally, the question becomes: what is "money?" One one level, it's merely a medium of exchange; some agreed-upon, fungible commodity - with, or without inherent value - that various parties have agreed to accept as consideration for one or more sides of a market agreement. On another level, it is "legal tender": some medium of exchange that the government has decreed constitutes satisfaction of an outstanding debt once the debtor tenders it in payment of that debt.
In other words, "legal tender" when accepted extinguishes the paid debt as a matter of law, without any further action on the part of either party to the relevant transaction. Any other medium of exchange will only extinguish a debt if tendering it constitutes performance pursuant to the contract by which the debt was created.
The distinction matters because something that has been declared to be "legal tender" will satisfy a debt once it's accepted even if there was no agreement or contract between the debtor and the person who accepted the tender. Something that has not been declared "legal tender" will only satisfy a debt if there is an agreement or contract between the debtor and the person who accepted the tender. This is important because it facilitates various sorts of transactions like the negotiation of so-called "negotiable instruments" (e.g., checks). This in turn matters because it allows people to effectively increase the money supply in limited amounts by issuing their own instruments that are essentially similar to "legal tender" itself, but which have that effect only with respect to the issuer, any endorsees, and the "holder in due course" (a term of art).
Bitcoin is not "legal tender" in that it cannot extinguish or satisfy a debt as a matter of law, and it most likely doesn't constitute a negotiable instrument, but that does not mean that it cannot be used as a medium of exchange between parties who agree to accept its tender as satisfaction of a debt owed to them by another party to the agreement.
