You said a CD and annuity are the same... maybe you're confused, but it's also possible they lied to profit off the commission.
With a CD, you deposit money and are paid interest until it's due, then you get your money back.
With an annuity, your initial deposit is gone forever. They make a bet on your life expectancy, and make payments over time. Life insurance companies make a lot of money on them, and that money comes from people who buy the products.
It's a really bad time to earn interest, since the Fed just dropped it's rates to 0%. The return of CDs will likely fall by a similar amount, since the bank can't afford to pay out the old rates.