You weren't necessarily doing anything wrong. The Garrettt and all other metal detectors that I have had exposure to only provide you with their best guess regarding the items that enter the magnetic fields they project.
Now many times the aluminum can will simulate different metals due to the shape of the crushed can, the piece of the can, in many cases of canslaw (mowed over can) the pieces each can register differently. The only way to absolutely determine what the item happens to be is to visually inspect it.
You have no doubt heard by now about the pulltab. It registers in exactly the same position as some gold rings will register in. So again if you get a consistent, repeatable beep, the best real discrimination is a visual inspection, meaning beep?-dig!
It is possible that due to the mineralization in your soil and the sensing done by the Garrett 300 that a can will always show up as a dime on that machine. You should still dig every one, however, by moving the coil left to right and back and forth, you may be able to determine that the size of the detected item is too large for a dime. (Frankly unless I'm really tired I'd dig it anyway, because the can might be masking a very good item that is underneath it).
Target masking is one of the reasons we're always told to re-check your hole. The item you removed might not be the only item in the immediate area and may have been masking or hiding a better item in the same area.
Keep at it, I think Mr. Garrett said spend at least 100 hours with your machine set to basic settings before you begin to experiment. This was said I think to make sure you have begun to learn the machine in it's basic detecting mode, and after you've done that you will better be able to understand what difference the changes in settings do when you're in the field.
Good luck and welcome to one of the most fascinating hobbies that exists. You're already on the best detecting site in the nation!
Be blessed!