Comoving distance vs physical distance In a recent post in Medium.com Ethan Siegel wrote the following:

"... as you look farther away, objects appear smaller until a critical point: a minimum size that objects will appear in our Universe, which occurs for objects that are somewhere around 15 billion light-years away. Beyond that, they start to appear larger again; if something comes from us close by or very far away, they will appear to be the same angular size on the sky."

Is this statement correct? The comoving distance $D_M = 15$ Glyr corresponds to about $z = 1.6$, ok. The author's text refers to the (physical) angular diameter distance $D_A(z)$ from which his conclusion is derived for an object of fixed size. But, from our point of view, since we are comoving with expansion, shouldn't we use the transverse comoving distance $D_M = D_A(1+z)$ instead to get the correct answer, i.e. that the size of an object is always decreasing with cosmic distance?
 A: The angular diameter distance is the distance to a standard ruler you would infer based on its angular size on the sky. (By "angular size", I mean the number of degrees an object takes up on the sky). In equations, given the size of the ruler $L$, and the angular size $\theta$, the angular diameter distance is defined as
\begin{equation}
d_A = \frac{L}{\theta}
\end{equation}
It is indeed true that the angular diameter distance increases with redshift for a while, hits a maximum, and then starts to decrease. Because of the way angular diameter distance is defined, an object with a larger angular diameter distance has a smaller angular size. This implies the result that Ethan writes. If you were to move an object further and further away from us, its angular size would decrease, then hit a maximum, and then start to increase.
To make a philosophical comment: the idea behind distance measures in cosmology is that there are many ways to measure distance in a non-expanding Universe that are all equivalent, but that are no longer equivalent in an expanding Universe. So, we can define multiple measures based on different non-expanding ways of measuring distance, that will all capture different ways of thinking about distance in an expanding Universe. The key things to pay attention to are how these measures are defined, and how they are related to each other. You shouldn't necessarily think that angular diameter distance gives you an "intuitive" definition of distance (personally I find comoving distance much more intuitive); it's just the distance you would infer for an object given its angular size.
A: After some investigation about my question I found that the statements of Ethan is correct and corresponds to the textbooks of cosmology. I realized that the distance DA(z) is the observed cosmological distance to an object of a fixed transverse size at redshift z, whereas the distance DM(z) is the distance to a linear (expanding) transverse separation in space. The latter does not apply for calculation of the angular diameter.
