No, I am not talking about where the duck-billed platypus fits on the evolutionary tree. I am talking about something even more basic: the platypus defies taxonomy itself. In other words, the fun of the platypus is that it does not easily fit into any attempt to categorize its species scientifically.
It is considered to be a mammal, but it has many characteristics that are highly unusual for mammals. It lays eggs. It has webbed feet. It has a bill that is different from the beaks of birds and the mouths of animals. It is venomous. It uses electrolocation. Its eyes are more similar to fish eyes than to the eyes of most other mammals. It is warm-blooded, but its average body temperature is lower than that of most other mammals. It has ten sex chromosomes instead of the usual two.
To be honest, I care little whether it is best to classify the platypus as a mammal or not. The point is that the platypus reveals the difficulty of imposing overly simplistic organizational systems upon the world. The animal world does not easily fall into clearly differentiable categories.
Another example of complex organization is the shape of a tree (the plant, not the evolutionary diagram). If a tree of a particular species is left to grow by itself in an open field, it will almost always conform to the same general shape as every other tree in that species. However, if you stand beneath the tree and look up, you will quickly realize that the placement of each branch and leaf within that tree, although following certain general patterns, is completely unique and unpredictable.
As humans, we tend to squeeze everything we observe into simplistic categories and patterns. Of course, the world exhibits a high degree of order, but it is the order of a tree, not the order of the Dewey decimal or Library of Congress book classification system.
As a result, we need to come to the world, reality, truth, people, God, etc. more as observers seeking to understand things as they are. When you do, you realize that everything is a platypus. Enjoy the oddities of life.