Why does Ramadan come 13 or 14 days earlier each year than its Gregorian date?

Years vary between solar and lunar, with the Gregorian calendar relying on the former, while the Hijri calendar relies on the latter. The lunar calendar is obligatory to follow, as Allah the Almighty says: "It is He who made the sun a shining light and the moon a [derived] light and determined for it phases - that you may know the number of years and [account for] time." The sun is for determining days, and the moon is for determining months and years. And Allah the Almighty's saying: "Indeed, the number of months with Allah is twelve months in the register of Allah [from] the day He created the heavens and the earth; of these, four are sacred. That is the correct religion." This indicates that this calendar is the straight law. And Allah the Almighty's saying: "They ask you, [O Muhammad], about the new moons. Say, 'They are measurements of time for the people and for Hajj.'" This shows that they are timings for all people's religious and worldly affairs.