I post few screenshots to explain it better.
The parent object “GameModes” has s specific size and anchor. Also, it’s pivot is on middle-left.
When I select the child “TexasHoldem”, you can see that the anchor is placed on the pivot of the parent, but the object, in position [0, 0, 0] is not centered on the anchor.
So, or the anchor arrows are wrong, or the position is wrong.
I’d go for the former.
Open “Anchor Issue” scene and select the child called “AnchoArrowsAreWrong” and see that the arrows of the anchor are on the left (aligned with the pivot of the parent).
The position of the child in (0, 0, 0), and anchor is set as “Center”. So something is wrong.