The argument is that under rate expectations, all bonds should have the same return over different horizons. The implication is that bond yields will equal (roughly) the geometric average of the short rate (adjusting for various yield conventions).
If they try to peg a particular bond issue at a yield that is inconsistent with the path of short rates, that is assumed to be impossible. The mechanism why this would hold is straightforward.
- If the pegged yield is too low, the issue would have a negative expected return versus cash (short-term instruments). The private sector would sell all of that bond to the central bank. The Fed would end up owning the entire amount outstanding of that issue (which makes its "market price" a philosophical question). This might be referred to as a run on the bond yield peg.
- If the pegged yield was too high relative to expectations, bond market participants would keep buying the issue until the central bank has no more to sell. It would then lose its ability to influence the market price lower (assuming the central bank does not want to get involved in short-selling).
In practice, the uncertainty around rate expectations by investors prevented such extreme outcome during the period when the Federal Reserve bond yield peg was credible. (Since no one is completely sure about the expected path of short rates, investors will not dump their entire bond portfolio, or proceed to buy up all of the central bank's holdings.) However, once the commitment to keep short rates low was questioned by the Fed, the peg was abandoned before such a "run" started.