Why can't I directly short the bond market?

It is possible to short bonds - you just need to find someone to borrow the bond from, someone to buy it, and keep track of where the interest payments should go. There's no "exchange" for bonds, so brokers would have to keep track of all of this, and there's not a big enough market demand to create the infrastructure for retail shorting.

Short Treasury ETFs, derivatives and CDSs may provide enough liquidity for bears to effectively short the two main factors for corporate bonds (interest rates and default risk) without having to keep track of coupons, margins, interest, etc.

If there were enough retail demand for shorting individual bonds, someone would step in and fill that supply gap.