Can't Draw Black Line (Result is Feathered)

Try using the Pencil tool instead.

To draw a straight perfectly horizontal or vertical line, click the start point, hold down Shift, and draw.

I tried this with Pencil size 1px and got none of the gray like in your example. However it might just be that it worked with my particular file dimensions  (2400 x 3000 px, resolution 300).

What are these dimensions in your file?

I noticed your file is viewed at 492%.

I created a blank file, set the view at that percentage, drew out a 1px line like yours, and got the same jagged look:

However when viewed at 100% the line is sharp with no jaggies, and it also prints with no jaggies.

I've seen this happen many times with other shapes and other tools such as Brush and Text, where the file is viewed at other than 100%.

Could this be what you are seeing?

Try the brush tool, using a hard brush.

Left click a start point, then hold down the shift key, then left click at the end point.