From curriculum (vol 4 page 413), it says “A fixed annuity locks the annuitant into a portfolio of bond-like assets at whatever rate of return exists at the time of purchase. This scenario creates some interest rate risk […]. […], he or she may be tempted to delay annuitization until interest rates rise.”
Why rising interest rate would benefit the annuity and tempt to delay annuitization?
If you are long a fixed rate bond and you get out before maturity you face interest rate risk. The risk of getting out the bond you own at the wrong time and entering another bond at the wrong time.
And if market rates are higher than the annuity rate, you may tempted to do so (delaying annuitization means delaying the conversion lump sum you paid for annuity into periodic income payments).