This interaction is seen in many nutrient combinations. High intake of zinc can deplete copper and iron. High intake of cadmium can deplete zinc, copper, and probably silver. High manganese can deplete chromium. High sodium can deplete potassium and probably lithium.
High calcium can deplete magnesium.
The list goes on and on. If you begin supplementation with anything but the most deficient nutrient, then this nutrient will get more depleted and the disease condition will worsen. When I had hyperthyroidism and was experimenting with taking different nutrients, it seemed that everything I tried made it worse. Several nutritional books and my nutritionist doctor recommended zinc, but this made the condition much worse. Iron made it worse.