While YMMV, a fear response is a choice. You can have all the rational reasons to be afraid (like the bottom of your hierarchy of needs being unmet) and choose to act out of cold rationality rather than fear. Then it becomes a self-fulfilling prophecy - if you can act without fear even when there is justified reason to be afraid, you will be able to easily do so when it isn't justified.
"... is called a delusion". What I am suggesting is not delusion, it is mindfulness and cutting through delusion. When one is presented with something that elicits a fear response (whether the stimulus is rational or not) the goal is to quiet all of the "lizard brain" reactions, and instead formulate a well reasoned response. "Fear is the mind-killer" - while from fiction, still rings true to me - if you react out of fear you will short-circuit internal processes that are far better at long-term reasoning even when at the expense of short-term comfort.
I'm sorry, but that is delusional. It is not possible for humans to forego emotion in favor of logic.
It's really just about giving yourself enough time to think before you respond. That's the entire difference between a reaction and a response. You can use dialectical and cognitive behavioral therapies to help develop the tolerance to do that. Mindfulness and meditative practices like those in zen buddhism have proven helpful to me as well. Perhaps you're taking an extreme interpretation of my using the word "logic" and instead you could use "wise mind" or even just "considered thought" as the response in lieu of an emotional one.
Where I come from, "hav[ing] all the rational reasons to be afraid" and pretending otherwise is called a delusion. I prefer to see the world as it is.