Arborio is a short grain rice treasured for its high starch content (and its toothy, or chalking core). When made into risotto or rice pudding, the starches slough off the exterior and add thick creaminess to the dishes. Don't rinse those starches off!
For other types of rice and other dishes, you want fluffy individual grains‚ not starch. That's when you do want to rinse the rice, as you have been doing.