Let me get this straight: This "logical" argument is that because I can think of a perfect being, it must be real because I can't imagine a non-existent perfect being? Because that's the biggest shit argument I've ever heard. Why did it take several hundred years to disprove?!
In fact, I can disprove God using it.
Taking the Ham Sandwich example. A Ham Sandwich is defined as ham between two pieces of bread. However there are many types of Ham: Smoked, boiled, cooked, honey glazed, etc...
And even bread has many different versions: white, wheat, oats, grain, Italian, French, etc...
So how could we define the perfect ham sandwich?
Well, the most perfect sandwich is that which is greater than any other and can't be better. But since everyone has different tastes, what is "best" is impossible as some will find wheat bread less than white while others will feel the opposite. And what about additions? Cheese, lettuce, tomato, mayo, etc...
So if we ignore everyone who doesn't like any ham sandwiches, we still have too many people and too many tastes to have one single ham sandwich that is perfect for everyone. So, it's impossible to imagine such a sandwich. However, when a sandwich does not exist, it can be everything at once. An imaginary sandwich doesn't need to conform to any one person but can be any kind of sandwich, based on what the person wants. This, in fact, is the only perfect sandwich since no other sandwich can be better than every sandwich combination.