Here's why:
* Cyber Dragon's effect: Cyber Dragon's effect is a Continuous effect that activates when it is Normal Summoned or Special Summoned. It doesn't have a timing clause that allows it to be activated during your opponent's turn.
* Timing of effects: Effects can only be activated during your own turn, unless they specifically state otherwise.
Possible misconception:
You might be thinking of "Cyber Dragon Infinity," which has a special effect that can be activated during your opponent's turn. However, that is a different card with a different effect.
In summary: Cyber Dragon can only be activated when you have control of the turn.