My understanding is that as interest rates go up, the yield offered by bonds also increases (in response).
If the yield of bond increases, then why are people selling bonds?
Bond prices and interest rates have an inverse relationship. When rates increase, bond price declines, and vice versa.
Suppose you bought a bond with a rate of 4%. At a later date, interest rates have increased and now, a bond of the same credit quality and type is issued with an interest rate of 6%. Why would anyone buy the 4% bond instead of the 6% bond? Therefore, the price of the 4% bond is reduced until it yields 6%.