First off aspect ratio is the ratio of the short side of an image to the long side, I shoot with al full frame camera so my images straight out of camera are at a 4x6 ratio. The length of the long side of the image is 1.5 times the length of the short side. Once you change this ratio you are manipulating the image, unless you choose a full frame size such as an 8x12, 16x24, or 20x30. If the larger side can divide into the smaller side and equal 1.5 you know it will be a full frame image with no cropping expected.
Take a look at the diagram below provided by Cornicello Photography. The various outlined colors show where that particular image would crop compared to a full frame image which will reveal the entire portrait.
Now lets take it a step further and show you an actual image and how it effects the overall look of the portrait at various sizes. Rachel with Rachael Myers Photography was kind enough to share this visualization of the same image cropped to various portraits sizes. I think she did a fabulous job, thank you for sharing Rachel!
Cropping can be quite confusing so I hope this litlle exlplination helps you better understand why every image will not ideally work with every portrait size.