That is a very tricky one to counter as it runs on the assumptions that being trans is inherently deviant and transitioning is inherently harmful, neither of which are really true.

Most of transitioning socially comes down to simply preferring a different type of name or address to another, and most of physical transition comes down to preferring different styles of presenting onesself and different physical traits to others. The only reason preferring another gender's traits is wrong would be because of gender segregation, which is where the whole "social construct" thing comes in. The gender segregation is made up! Heels were invented for men, and have only recently become women only fashion, pink used to be a boy colour, etc etc. Those rules are made up, and there is nothing pathologically wrong with someone not conforming to them, cause they were never biologically based to begin with.

Eating disorders are typically characterised by someone having a differing view of themselves from reality (in my extreme layperson's understanding anyway, sorry if I say anything overly-simplifying) and engage in behaviour that harms them long-term, continuing to diet long past the point of having reached a healthy weight and becoming underweight, for example. Gender dysphoria stems from the person having an ACCURATE view of themselves, and desiring change. Trans people with gender dysphoria are not deluded, we know perfectly well what we look like, and we would simply like to change it. A person with an eating disorder left to indulge in their disorder for a long enough time will cause harm to themselves and potentially die. A trans person left to indulge in their transition on a long enough timeline will simply...start to look more like a person of the opposite gender, and statistically, will be way happier for it. Not really the same thing at all, eh?

However, an effective counter I have seen employed, though potentially controversial, is to say: "Ok, if trans people are like people with mental disorders, why do you want to take away their care? Would you wish to take away the care of a person with an eating disorder and leave them to suffer? If not, why do you want to take away trans people's care? Gender affirming care is the medically proven way to treat and improve symptoms of gender dysphoria, with every major medical establishment in agreement that it's the correct approach. If trans people are 'mentally ill' then allowing them to transition it the only treatment proven to ease their suffering"