The trap has nothing to do with the call itself. It is that the call period and the maturity date are two different dates, and marketing language mentions only the first. The SEC prints it as a "Potential Pitfall": "Don't assume that a 'federally insured one-year non-callable' CD matures in one year. It doesn't. These words mean the bank cannot redeem the CD during the first year, but they have nothing to do with the CD's maturity date. A 'one-year non-callable' CD may still have a maturity date 15 or 20 years in the future." The same guidance notes that many people "fail to confirm the maturity dates for their CDs and are later shocked to learn that they've tied up their money for five, ten, or even twenty years", and tells buyers to ask to see the maturity date in writing.
The economics run one way, and it is worth stating without euphemism. A bank calls a CD when it can refinance the same money more cheaply, which means after rates have fallen. The depositor then holds cash and a market paying less than the CD did. If rates rise instead, the bank has no reason to call, so the depositor keeps earning the older, now below-market rate for the rest of a term that may be very long. The FDIC states the consequence plainly: "A callable, fixed-rate CD could undermine your ability to lock in an attractive, long-term interest rate." The higher rate a callable CD advertises is compensation for handing the bank that option.
A call is not an early withdrawal, and conflating the two produces the wrong expectations in both directions. Breaking a CD yourself triggers whatever early withdrawal penalty the deposit agreement sets, which can exceed the interest earned so far. A call is the bank exercising a contractual right, so principal and accrued interest come back intact and nothing is forfeited. What a call does not do is give the depositor any choice about timing, and the timing will be the least convenient one available, because the bank chooses it for its own reasons.
Two adjacent features often travel with callability and should not be assumed away. The FDIC observes that "most market-linked CDs do not allow for an early redemption" and that "[m]any market-linked CDs accrue interest only when the CD matures, not every day or every month". A CD that is both callable and non-redeemable by the depositor offers an exit to one party only. The FDIC also warns that a rate far above the competition can be a marketing device, describing a pattern in which a small bonus is added to an insured bank CD to attract customers who are then offered uninsured, long-term products. None of that makes a callable CD improper. It makes the deposit agreement, and specifically the maturity date and the call schedule, the two things worth reading before the money moves.
The general machinery of a call right, including how issuers price it and what yield-to-call measures, belongs to callable bonds and bond yield. What is specific here is that the instrument is a federally insured deposit rather than a security, so the call returns cash at par rather than exposing the holder to a market price.