Both DSL and Cable are Broadband services. FACT.
The FCC defines broadband service as data transmission speeds exceeding 200 kilobits per second (Kbps), in at least one direction: downstream or upstream.
And, cable isn't that fast. Fiber is much faster (for example, Verizon FiOS). I live in the chicagoland area and the highest cable speed offered is 6mbps, the highest DSL speed is also 6mbps. So, again, how is cable broadband and DSL not broadband? And if you compare your so-called "fast broadband speed" to the majority of other developed countries broadband services, they're moving at a rabbit's speed while you're moving at a turtle's speed. The US pretty much has dial-up service compared to Japan, Korea, and several European countries. Heck, Canadian has faster speeds than we do.