The classical elements of fire, earth, air, and water have been replaced in modern times with the periodic table of elements in the minds of most. Are the ancients dead wrong, or are we misinterpreting their meaning? In order for something to be an "element", it must be the simplest part of a system, indivisible. None of the 4 elements meets that criteria in a literal sense.

The classical elements are therefore obviously symbolic, if they have any validity at all. So what do they symbolize?

I kind of think they are "macro" symbols which represent multiple things. One almost perfect correspondence is in the 4 states of matter; Air=Gas,Water=Liquid,Earth=Solid,Fire=Plasma. But an even bigger idea would be Fire=Will,Earth=Matter,Air=Information,Water=Change, because those could be seen as primal elements. Any other ideas?

They could be considered the human elements.
Fire=emotion and/or passion
Earth=logic and/or knowledge
Air=imagination and/or creativity
Water=spirit and/or faith

Just a thought.

I think that, if one looks at the hisiorical context of when the four elements became to be discussed, the Pre-sokratics had one foot in the older world of mythological/ quasi-religious perspectives, and the other foot tentatively finding its ground in a new way to explain the world through (more or less) rational causation and first principles ("Wisdom, First Philosophy). It is not unimportant than, at least from what is extant, many of these expositions took the form of poetry (for example, Empedokles), where the distinction between being and seeming was less than clear, and "cause" was far from defined.
Some, again, found the answer in one or more of the four elements, others in primitive atomistic or dualistic theories (Love/Strife).
As Aristotle argues (Metaphysics, Book I) the earliest monistic thinkers were tied down to the conception that the only things that existed were material, and the only question to be decided was what was the ultimate form of body from which everything was a transformation.

Now this is one possible way of viewing the question and is more or less from a historical viewpoint.

But the early writers have been a great source of all sorts of interpretations because for the most part, what we have of what we think are their writings, are extremely fragmentary and found in brief quotations by later philosophers.

Zarathustra

I'm all for "Water=spirit and/or faith" ! (No reason for using the bunny - just think he's cute and never ever get a chance to insert him somewhere).