The assertion states that discharge printing of dyed polyester fabric is not possible, which is incorrect. Discharge printing is indeed possible on polyester fabrics; however, it requires specific discharge agents, and care must be taken during the process to avoid damage to the fabric.
The reason given for this assertion is that discharging agents damage the polyester fibers significantly. While discharging agents can affect the fabric, the damage is not typically significant if the process is done correctly and with the appropriate agents. Therefore, both the assertion and reason are incorrect.
Final Answer:
\[
\boxed{\text{(C) Both [a] and [r] are false}}.
\]