Fight or Flight?
We’re more complex than that
So you know that when under stress, our instinctive reaction is to ‘fight or flight’, right?
“The fight-or-flight response to stress is a well-documented phenomenon that has been widely observed in humans and non-human animals.” 
However, whilst that is an accepted truth (at least it was for me), and the phrase ‘fight or flight’ is widely used, it turns out that, in reality, people are rather more complex that. Rather than just those two options, we have several other instinctive reactions to stress.
So how come?
Well, first off, because our autonomic nervous sytem, which regulates body functions below the level of consciouness and so drives our response to stress, comprises two systems: the sympathetic system and the parasympathetic system. The sympathetic system prepares the body for action — ‘fight or flight’ and the parasympathetic system prepares it for repose (‘rest and digest’).
Our ‘fight or flight’ responses “go along with arousal, activation of the sympathetic nervous system” . But, as well as ‘fight or flight’, we have a third instinctive reaction to stress: ‘freeze’.
Freezing is a stage of attentive immobility. It is characterized by bodily immobility and heartrate deceleration. Together these can buy us the time to prepare for ‘fight or flight’ actions (eg attacking or avoiding the predator).
“Freezing is most likely to occur when the threat is still at a distance. It is thought to optimize the animal’s attentional processes serving the selection and preparation of appropriate sympathetically dominated fight-or-flight responses to cope with threat.” 
So, rather than simply ‘fight or flight’, some people refer to ‘fight, flight or freeze’.
But that’s not the end of the story.
Why? Because sexism.
Tend and Befriend
For many years — several decades in fact— the research on the nervous system behind the ‘fight or flight’ response was conducted overwhelmingly on men. (Reminds me of what Caroline Criado Perez showed about ‘the gender data gap’ in her book Invisible Women.)
“Up until 1995, research investigating the fight-or-flight response had been done primarily with males, females only constituting 17% of the participants.”  Only later studies, like a famous one done by Taylor et al. began to hone in on women’s coping mechanisms for stress. They identified that female’s reactions to stress often didn’t coincide with the ‘fight-or-flight’ model. Rather, their responses “are more marked by a pattern of ‘tend-and-befriend.’”
The tendency to “tend-and-befriend” involves investing into social networks after stress, offering help to a delimited group of people in order to seek and offer mutual protection during anticipated or experienced threats:
“Tending involves nurturant activities designed to protect the self and offspring that promote safety and reduce distress; befriending is the creation and maintenance of social networks that may aid in this process.” 
However, our story isn’t quite over yet.
It is not only women who nurture and protect offspring and who seek social support and attention. And it turns out the ‘tend and befriend’ stress response is not female-specific either. A tend-and-befriend response has also been identified in males .
“When talking about male and female stress responses, it can be easy to fall into the idea that the two are mutually exclusive. That isn’t true. It’s better to think of these two things as tendencies.” 
“It is not, however, clear whether these responses are due to sex, sex hormones, gender, or both — or perhaps even influenced by how our own gendered assumptions factor into our research designs and the interpretation of findings.*” 
So it definitely isn’t just a question of ‘flight or flight’.
For all of us, our instinctive stress responses are more complex than that.
FWIW Some people (I guess they like allieration) also say that we have a ‘fawn’ response, which involves trying to please a person — the predator — in order to avoid conflict. Other people call this response ‘appease’ (I guess they’re not so fussed about alliteration). Or is that another separate stress response? Furthermore, some people also identify a ‘fold’ or ‘faint’ response (more alliteration) of complete shutdown/collapse. So that could be another category, or perhaps it’s two more? Or perhaps, rather than seeing it as complicated, and keeping on adding categories, our system is complex.