What is the most expensive legally available alcohol / drink in the world (per unit)? And why does it command the price?
Prices for rare or unique items are usually nearly meaningless numbers. What an item fetched at auction last week may have no bearing on what you might be able to buy it for today (possibly it would be literally priceless), and no bearing on what it might sell for tomorrow if it went to auction again. That said, a 1947 Cheval-Blanc last sold at auction in 2010 for £192,000. Who knows what Thomas Jefferson's Chateau Lafite 1787 would sell for if it came up for auction now (it sold in 1985 for $160,000).
If you restrict it to something you can actually buy now at retail, I think it would be tough to beat the 50 year old Balvenie (~£30,000) or 50 year old Macallan Lalique (~£50,000 if available?), but prices will be highly retailer dependent.
Novelty bar drinks will probably be more expensive by volume, if anybody actually pays for them... but if you disqualify Diamond Is Forever from the Ritz-Carlton in Tokyo ($22,600) since you're paying for a $16,000 diamond inside the drink itself, and also disqualify drinks with any precious materials other than the liquids themselves (e.g. The Gigi from Gigi's at Mayfair for £8,888 gets you a bit of gold leaf) and further disqualify "profits go to charity"-type drinks (you can taste the Macallan Cire Perdue¹ for $64,000 at the £10 bar (lol) of Montage Beverly Hills hotel), you're probably left with whatever made-for-publicity drink currently holds the record. That might be Salvatore's Legacy at £5,500 from Playboy Club in Mayfair... but at this point, does it really matter? The prices would seem to just be part of the gimmick and a way of keeping score.
To try to answer the "why" part of the question explicitly, a price is only reflective of value to the extent that both a buyer and a seller can agree to transact at it. A ticket price only indicates willingness on a seller's part, and shouldn't be taken as evidence that it can in fact "command" that price. That said, while production costs (including storage, wastage, and opportunity costs) are a big reason why older wines and spirits tend to cost more, at the top end, rarity and perceived prestige will also play a big part. At auctions, though, most of it will come down to a few people with money who all want something of which only one exists. It's similar to how a print of what to my admittedly philistine eyes looks like a boring photograph of a not-particularly-pretty section of river can sell for millions.
1: the Cire Perdue bottle itself was disqualified at the outset for being cheaper per liter than the wines and also not available at retail.