Why Cruciferous food is bad for Hypothyroidism?

If you have hypothyroidism (underactive thyroid), you may have been told to avoid cruciferous vegetables such as

These vegetables have been shown, in certain situations, to interfere with how your thyroid gland uses iodine.

Cruciferous vegetables, such as broccoli and cabbage, are full of fiber and other nutrients.

but they may interfere with production of thyroid hormone if you have an iodine deficiency.