Here's why:

* Main Sequence: This is the longest and most stable phase of a star's life. During this stage, the star is fusing hydrogen into helium in its core. This fusion process generates outward pressure that counteracts gravity, creating a balance. The core is relatively hot and dense, but the fusion process keeps the density from increasing further.

* Red Giant: After the main sequence, the star enters the red giant phase. Here, hydrogen fusion shifts to a shell surrounding the core, and the core itself begins to contract. This contraction increases the core's density significantly.

* Other Stages: As the star progresses through later stages (like the asymptotic giant branch and planetary nebula), the core continues to shrink and become denser.

Therefore, the main sequence stage is when the core of a sun-like star has the lowest density due to the balance between fusion and gravity.