Analyzing threats, the goal is to discern the adversary’s intent and beliefs about the state of play.
(and either ignore them, defend against them, or counterattack, NEVER comply. Compliance is death, sometimes literally. More on that later.)
Smart adversaries rarely make specific threats, and even more rarely do they make threats they intend to carry out.
Why? Because ultimately the adversary’s goal is to control and/or destroy you, and they will do everything they can towards that goal —
regardless of whether you comply with a threat or not. Potentially giving you an option to stop this is not something an adversary will do. Indeed, threats are often counterproductive as they give you notice to defend against an attack.
Therefore, if the adversary threatens to paint your house pink unless you marry his daughter, you can conclude a few things: the adversary would rather not paint your house pink (because he doesn’t mind if you implement security measures to prevent that), and the adversary wants you to marry said daughter so badly he’s willing to risk the bridge-burning that threats entail to achieve that.
(This inherently duplicitous nature of threats — “do this thing I want or I’ll do something I don’t want to do” — illustrates just how much security is a mental game, while the real-world manifestations are often just there to keep score. Someone once told me to stop seeing it all as a game; I replied that it was the only way to stay sane.)
Depending on the adversary’s cleverness, threats may also suggest that the adversary has concluded that other, more-likely-to-succeed routes of attack are undesirable — or they may have already failed. In the latter case, threats can be a positive indicator for the defense.
Now, I said that you should NEVER comply with a threat. This is because the adversary’s goal tends to be controlling you and never letting go. The exception, of course, is in e.g muggings, where all signs indicate the guy just wants your wallet so he can buy a fix. In that case, better to lose your wallet than gain a knife wound. (and you can proceed to call the cops ASAP in hopes they’ll find the guy and get your wallet)
However, if there’s ANY indication an attacker wants “more,” or wants to control you — “come with me or I’ll kill you,” the usual rule comes back into force. Better a knife wound or a bullet in your arm than watching him eat your liver (or soul) with a nice glass of Chianti.