Oh I'd be happy to explain! The thing here is that 1 and 3 are true statements stitched together in a misleading way.

The assumption that I'm making but not proving is that poor diet and sedentary lifestyle contribute to negative health outcomes. Furthermore, excess body fat is strongly associated to said poor diet and sedentary lifestyle (lots of calories, few nutrients in proportion to those calories, no burning off of said calories through exercise). I see this as invalidating 4, but of course I would need to provide papers showing the correlation and I'm going to be lazy and just state that these papers exist. Wikipedia has some OK links to said papers.

Notice that excess weight as an indicator immediately weakens the correlation since not every overweight person will experience negative health consequences as a result and we also need to figure out how to measure "overweight". So, there's some built in "fuzziness" right away (as noted by 3) but this is accepted because there's advantage in people being able to test at home with limited equipment AND excess weight is bad for a few other reasons (hard on joints, difficulty with accessibility, etc.).

With that in mind, reading wikipedia, and checking the linked sources leads me to believe that 1 is true. However, this observation does not undermine all metrics nor the practice, only BMI (this is my rebuttal to 2). It's just an invitation to try a bit harder. Waist to hip and waist to height ratio seem to do a better job than BMI, and body fat percentage (measured on a smart device or whatever) does an even better job.

These are my thoughts. I am not a medical professional and so constructive criticism is welcome!

Tl;dr 1-4 is basically a "bad apple spoils the bunch" style argument.

Oh the irritating crowd you're referring to can and will change the science (as they see it) like so:

1. Undermine BMI as a metric using the lack of association between the "overweight but not obese" category with negative health outcomes.
2. Argue that this invalidates the metrics for "obese" as well.
3. Argue that no metric has perfect 1.0 correlation of obesity and negative health outcomes.
4. Conclude that obesity is a social construct that is completely unrelated to health.

All while claiming they "follow the science"...

To the CS students out there: Yes, you must know how to solve this problem to prepare for a job interview.