Why do distant objects appear to move more slowly?

1. The problem statement, all variables and given/known data
This is not really a homework question and I am not sure if this should be in the Maths forum or Physics forum.

See the title.
For example,a plane with the same length and speed is moving at constant speed near and far away from me.
From my experience I know that the far plane will appear to move more slowly.Why?

3. The attempt at a solution
I have seen many people saying that as the distance from the eye increases,the distance the plane have to move across the field of view increases.That’s why it is moving slowly.
This does not make much sense to me.
I don’t have a proof based understanding of this.

One idea that came to my mind is that as the distance from the eye increases,as the plane goes from a point A to B(Eye is C),the angle ACB is less than the angle ACB it makes when it moves nearer to me.
So as the angle is less, the distance it moves on the image is less.
(I can’t explain this so well but I hope you understand what I mean)

My explanation seems too childish.If it’s right,can you make it make sense Mathematically?

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