Without knowing the nature of the secret, I can't really comment on that assessment directly.
In any situation where the character could benefit from revealing the secret, it's a disadvantage.
In any situation where the character might be coerced (or forced, or manipulated, etc.) into revealing the secret, and the secret would be damaging to them if discovered, then it's actually advantageous to be entirely unable to reveal it.
How those two factors balance out depends entirely on the nature of the secret and the likely consequences of its discovery.
In any situation where the character could benefit from revealing the secret, it's a disadvantage.
In any situation where the character might be coerced (or forced, or manipulated, etc.) into revealing the secret, and the secret would be damaging to them if discovered, then it's actually advantageous to be entirely unable to reveal it.
How those two factors balance out depends entirely on the nature of the secret and the likely consequences of its discovery.