Here's why.
You might have observed that the sun and moon appear to be same size when observed even though their size is vastly different. This has to do with basic trigonometry. If you join the center of earth to center of the sun and other line as a tangent to form a triangle . Similarly from the center of the earth join it to center of the moon and other line as a tangent to the moon. Now we have two triangles. Lets get familiar with some notations to make this explanation easy. Let the radius of Sun and moon be R and r respectively. Let the solid angle from Earth to Sun and Moon be the α and β respectively. The distance between the earth to Sun and Moon be D and d.
From these values lets substitute the radius and distance:
D = 149,000,000km
d = 384,000km
R = 696,340km
r = 173701km
Now to get the solid angle we need to take the twice of arctan of the ratio of Radius to the distance. From this we can see that the values are α = 0.534 & β = 0.518. These are extremely close. As the solid angle is same any object in between the solid angle touching the ends appears as the same size from earth. The minute difference in the solid angle is the reason we can see the Ring of Fire.
Here is a cool phenomenon that occurs due to the above reason. The ISS appears to be the same size from earth over moon and sun.
Pic: J.Mccarthy
Refer to the following paper for an complete mathematical proof for the occurrence of solar eclipse: https://www.ripublication.com/ijome16/ijomev6n1_02.pdf
Check out the following Video for an visual explanation of Solar Eclipse:
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