Why do people think rabbit ears will no longer work? The antennas will work fine; it’s just that some people who were using them might not get acceptable reception. But I’m sure some folks will do fine with them.
As for why they might be less useful I expect the primary reason is that people can tolerate a degraded analog signal, but not a digital one. So while some amount of static may not bother someone on the analog reception, the digital signal will be simply unwatchable — not even displayed by the tuner, most likely. Also it seems that some of the previously VHF channels changed to UHF for digital, so that may be part of the reason as well (‘rabbit ear’ antennas work best for the lower frequency stations).