The answer to 'why is my tree thin grass' is that the tree's roots are likely competing with the grass for nutrients and water, causing the grass to become thin and sparse around the tree. This is a common issue that can occur when trees are planted too close to lawns.
Some other common causes of thin grass around trees include the tree's canopy shading out the grass, the tree's roots growing close to the surface and outcompeting the grass, and soil compaction from foot traffic around the tree. To address this issue, you may need to adjust the tree's placement, prune the canopy, aerate the soil, or overseed the grass.