To paraphrase and apply an argument given by Doug Wilson for Reformed Kingdom Theology:
There are things that everyone can distinguish, and that are clearly distinct and unique but at the same time also cannot be separated, cannot be amalgamated, and cannot not exist on their own. An example of one of these is the 3 dimensions of an object: Height, Breadth, and Depth. The height of your house is obviously distinguishable from its breadth and depth. No one could confuse those or say they are the same thing. However, if you remove the height from the house you are not left with a very flat house. A house with no height is no house at all. The same is true for the breadth and depth. So, it is true that each dimension is distinct and easily distinguishable, but they cannot be separated nor amalgamated.
Now think about the Trinity.