BMI is rejected because it tells people they're obese and since its unhealthy, they need to change themselves. Noone likes hearing that. The truth hurts.
You'll see these common rejections: 1. Bodyfat loss is hard, so its claimed as not a good measure. 2. BMI has outliers so _mine_ being bad doesn't count. 3. Because not being obese does not provide data about health, they attempt to deny obesity as a poor health marker. This is almost always "you can't tell a skinny person is unhealthy" retort as an excuse to reject obesity as unhealthy.
They will not escape the evidence-based scientific truth that obesity is unhealthy.