You'd be pissed if they didn't use a cooldown, but you're upset that they use a different ability to help keep their HP up?

Defensive cooldowns are usually off-GCD and impact no part of your anything.

Clemency takes up MP and a GCD, which might not be that impactful if you use it a few times, but if you're regularly using it it will definitely lessen your performance.

Maybe you need to think of it this way - maybe you and the tank have different concepts of what 'safe' feels like.

This is also a bad argument. The number of times my health has dropped to almost nothing and I've been fine are waaaaaaaaaaaaaaaaaaaaaay higher than the number of times I've actually died. Push comes to shove, there are abilities that literally prevent you from being able to die for a short period of time. If you really think it's a life or death situation, then pop one of those. If you're not confident enough to let your healer do their job you're probably not doing content that requires expert use of it anyways.

The PLDs that use Clemency all the time might have a different concept of 'safe', but said PLDs are probably wrong.