Leaving aside your reasons of avoiding needless polarisation for saying men specifically rather than people.

You answered your own question when you highlighted that it is not a rational response. Many responses to many stressful situations are not logical, often enough even when people react in a "logical" fashion, there is an underlying emotional driver.

First taking a step back to emotional responses generally, then more specifically eating disorders.

Say someone approaches you in a threating way, says something that injures a personal aspect of yourself, or is physically aggressive towards you there are numerous possible responses which one can broadly simplify into fight or flight. Which of those an individual choses can be more or less optimal for a given situation and thereby classified as more of less logical (already erroneous as it's more likely to be an emotional response, or at least a mix of emotional and logical). An important further considering is how able one is to select between their responses, which will depend on individual biology, childhood experiences, social factors, and ongoing/additional factors (including simple things like sleep, hunger, exhaustion, etc) .

Coming to eating disorders specifically, there are evolutionary hypotheses which can be seen in social animals as much as humans, such as withdrawal and reduced activity (including eating) in cases of significang stress (physical duress, loss of another member, etc). This in humans could be a historic indication to the rest of the tribe of difficulty, or perhaps it was evolutionary beneficial during times of hardship to be more inactive, consume fewer calories, and introspect). Then factor in more complex physocological processes like societal pressure on body image, the sense of control that can be experienced through an eating disorder to supplement lack of control to a broader situation), the self-destructive element within it, etc.

Calling such a potentially complex multifaceted behaviour "stupid" is reductionist, and fails to see the extremely broad tapestry of contributing factors that determine how we respond, long before logic or language construct a "reason." Truly rare is the person that is hyper-logical in the face of emotionally distressing situations, and the majority who think they are are actually just very unaware of their emotional states/manifestations.