> Can someone not borrow against a bond?

Yes. But that cash has to come from somewhere. If there's less cash in the system in aggregate, those with it gain leverage. Which means they can get a higher rate. Which raises rates.

The leaky bit in this equation are banks. They can magic money out of nothing to lend against a bond. The patch to the problem is capital requirements.

so really what likely happens is that for every dollar of bond the fed sells, you're really only reducing pennies in circulation, given capital requirements for secured loans.