Your "equilibrium" argument has been invalidated. This argument was popularized by Henry Morris (1974, p.164), who used some calculations done in 1968 by Melvin Cook to get the 10,000-year figure. In 1968 another creationist, Robert L. Whitelaw, using a greater ratio of carbon-14 production to decay, concluded that only 5000 years passed since carbon-14 started forming in the atmosphere!.
The argument may be compared to filling a barrel which has numerous small holes in its sides. We stick the garden hose in and turn it on full blast. The water coming out of the hose is analogous to the continuous production of carbon-14 atoms in the upper atmosphere. The barrel represents the earth's atmosphere in which the carbon-14 accumulates.