Here is the main reason why you should not be using Photoshop for creating logos.
Photoshop can not create true vector images. Photoshop does have so called vector tools and can save some vector content in some formats, however, Photoshop will never create a true vector file. Regardless of how you create a file and save it, Photoshop always saves both vector and raster information. You can't create vector files with Photoshop. What Photoshop creates are vector containers with raster content. This is much different than a vector container with a vector content. If a square has a gradient fill. That gradient fill is raster based and it will suffer when scaling.
A vector based program like Illustrator, will create a vector shape with a vector gradient within that shape. That means when the shape is resized upon output, the gradient is recalculated to match the new boundaries. What Photoshop does is, upon output, it recalculates the vector container but only scales the raster contents in the container. This can result in "broken pixels" for the interior appearance.