My MacBook Pro is set to a resolution of 2880*1800 yet when I take a screenshot, the selection shows 1440*900. How is it halved?
MacBook Pros have Retina displays. This means that there are 2880x1800 physical pixels on your screen. However, as you have noticed, there's only 1440x900 logical pixels.
If the MacBook calculated logical pixels at the same size as the physical pixels, everything would be too small. After all, they're called Retina displays because the physical pixels are too small for the human eye to distinguish (theoretically at least).
In order to solve this problem, MacBooks and other modern devices use half the number of logical pixels when calculating the positioning of elements, but use physical pixels to actually display elements.
This is why you're getting conflicting pixel counts. When you take a screenshot, it will say 1440x900 logical pixels, but the actual image saved will capture the full resolution of 2880x1800. I know this because I'm currently typing this on a MBP with the same resolution and tested it for myself.
(Images are from https://blog.specctr.com/pixels-physical-vs-logical-c84710199d62, which has a more in-depth explanation if you're still curious.)
The image will always have the same dimensions as the screen or window being captured — a 1440x900 screen will create a 1440x900 screenshot.
Today's operating systems are resolution-dependent: everything you see screen is either being shown at actual size or has been rendered at some pixel dimensions. So, the size of objects on a computer display is entirely dependent on the pixel density of the display — a higher-resolution screen would make everything smaller.