Isn’t this kind of begging the question? It’s implicit in your reasoning that the CIA does exactly what I’ve claimed they generally don’t do.

Anyway, the point is that I don’t think you have to dig very deep these days to find plenty of instances of geopolitical power X doing bad things, so I’m not sure why the CIA would bother lying to stir up shit against them when they could tell the truth just as easily, with the same result. This assumes their purpose in releasing any information at all is to influence public opinion, not increase transparency, as the latter would probably mean divulging uncomfortable truths. The former does not—they can release exactly what they want, and no more.

On the other hand, flatly denying you’ve done a bad thing is a form response for governments and corporations (and politicians) at this point, even when it’s risible on its face. If you’re the guy responsible for putting those comms together and you admit wrongdoing, you’re never working in this town again. Simple as that. Deny, deny, deny. Deny everything. (Isn’t that a one-off X-Files title card?)

Has the CIA lied? Absolutely, though I’d guess far more often (orders of magnitude?) by omission than by outright explicit falsehood. The latter goes against the same ass-covering impulse that drives the bullshit denials. My brief comment above is meant to be a general observation on the sorts of public communication games the CIA and similar organizations tend to play, not an absolute truth or bible for living your life.

> So when the CIA tells me some foreign government is doing something bad, I should believe them?

Honestly, yes.

> Then when the CIA denies they lied about the foreign government was doing something bad

When have they done this? A few times probably, but not really a high percentage.

At any rate, P(CIA telling the truth about a foreign govt|foreign govt is doing something bad) is much higher than P(CIA lying about foreign govt|foreign govt is not doing something bad). The rational thing is to put higher weight on such statements than when the CIA is trying to cover their own ass.

The ratio of lies isn't as important as when they do lie. Their willingness to lie on big things means that they are never trustworthy.

99 reports could be truthful but the 1 lie that leads to war is enough to ruin their reputation.

There's a difference between them telling what they think is the truth, and them actually knowing something and telling it. The whole "Havana Syndrome" thing might actually be them telling what they think is the truth (Russian/Cuban conspiracy to use secret weapons to give headaches to people), even though it's complete nonsense.