Emotions are not bed rolls, or a ball, or other stuff. They are not electricity, to be tuned by dial or turned off by switch.
The are the root of all choice. This can be hard to accept. In general, humanity colors emotion as weakness. Finding out that we aren't quite the rational animals we think we are can be disturbing.
It's fairly well documented, scientifically. Brain damage to the amygdala tends to result in loss of affect. People with such damage show little emotion, and report feeling little. Such people also tend to have a marked difficulty making decisions between options. This strongly suggests that what we feel about a thing is more important than what we think about it. It goes to explain why facts don't persuade people.
For what ever reason, Faye didn't feel what she would need to feel to "be supportive" in that moment. Moreover, she did not feel anything that would have driven her to fake it, for Angus's sake.
She was faced with the choice of making a sacrifice, or walking away. Despite our cultural fetish for sacrifice, it isn't always the right choice.
Faye chose poorly, in that she didn't tell Angus what she was thinking. But she chose correctly, as far as the timing. Trying to fake it would have only increased her disquiet. It would rapidly have become resentment.
By creating a bad situation, immediately, she prevented a worse situation later.
As unfair as that may be, Angus helped to create the crisis. First by ignoring the signs that the crisis was coming. While Faye helped him do that, his own actions show he wasn't really buying her assurances. But he let that slide. But more importantly, he forced the issue at the time of crisis.
To use your metaphor, he didn't just say, "that looks like a fun mountain to climb." He brushed off any worries about whether the proper supplies were on hand, whether he or Faye were in shape to handle the mountain, and Faye's fear of heights. He also quickly implied that being afraid was a moral failure on Faye's part, and--at the critical moment--offered only the choice "commit to climb, now, or walk away."
There's a reason that strip is titled "You Idiots." Angus AND Faye handled it poorly. But there's no certainty, had they performed better, the results would have been different.