Why is money in circulation a liability of the central bank?

From BOJ

The Bank started to issue banknotes in 1885. At that time, the banknotes were convertible notes whose convertibility to silver was guaranteed. Thereafter, when the gold standard was adopted, the banknotes became convertible to gold. Under these systems, the Bank was required to hold gold or silver equivalent to the amount of banknotes issued so as to meet the demand to exchange banknotes for gold or silver at any time. In this sense, it can be said that the banknotes represented the liability certificate issued by the Bank. Given this, the Bank recorded gold and silver as assets and banknotes as liabilities on its balance sheet.

These reserve requirements were later abolished. In the meantime, a view began to take hold that the stability of the value of banknotes should be maintained through the appropriate conduct of monetary policy by the Bank, rather than through a direct link with the value of assets held by the Bank. In this regard, banknotes continue to represent the liability certificate -- of which the credibility must be ensured by the Bank -- and are still on the liability side of the Bank's balance sheet. Such accounting treatment of banknotes is commonly applied among other major central banks.

The question presupposes an error: not all the money in circulation is a liability for central bank.

Your statement is correct... except for the part of new money "loaned out to the commercial banks by buying treasury bonds". The new money created by commercial (i.e. non central) banks is backed with their own deposits in central bank just for the percentage defined by "fractional reserve requirements" (or the precautionary reserves decided by the bank itself, if higher). [There is another misstatement with the expression "by buying treasury bonds", but it's outside the point here.]

So, the money in circulation (ambiguous expression itself, as long as it could refer to different measures or categories of money: google m1, m2, m3) is a central bank's liability only in the amount of hard cash (M0) plus the part of the current deposits which the commercial banks, in turn, keep backed by deposits in the central bank.

As a proper accounting question, it's almost a definitional question: only "the money" which is backed by central bank liability sums up as a central bank liability.

The rest of the money issued by commercial banks is backed by their own liability. In fact, all the money issued by commercial banks is backed by their own liability, but the fractional reserve kept as deposits in central bank are assets that offset the gross amount.

Additionally, and contrary to what we commonly think, those liabilities do mean that banks, central and commercial, owe those sums, even though after the end of convertibility nobody will, nor can, draw the credit from the central bank, at least not in other form than in current money itself (returning to initial position). Anyway, those liabilities could be claimed from a bank (commercial and, theorically, also central) by transferring the deposit to another bank, which causes the liability itself being also transferred from one bank to another.

Finally, we can answer your question: money in circulation is a liability for bank system (central as well as commercial banks), from the point of view of bank balance sheet. Interestingly enough, that is why creating money doesn't mean creating net wealth at global level, as an asset and a liability spring at once.