The first few things one may have in mind when thinking about Zakat are money, silver, gold and the zakat or sadaqah of fitr after Ramadan.
Nevertheless we find that zakat must also be paid from some kinds of cereals and some kinds of cattle etc. while it is excluding others for example I couldn't find any statement saying that we must pay zakat from horses while Allah says:
Beautified for people is the love of that which they desire - of women and sons, heaped-up sums of gold and silver, fine branded horses, and cattle and tilled land. That is the enjoyment of worldly life, but Allah has with Him the best return. (3:14)
were almost all these things are mentioned and all these things are not only enjoyment of worldly life, but also considered as wealth.
For example having a stable full of horses or having a garage full of cars looks like a big wealth on which zakat would be a profit for many poor Muslims. But it seems paying zakat from horses is explicitly rejected in the sunnah and a qiyas (analogy) on cars wouldn't therefore make sense.
Is there any explanation for the concept of what makes an item due to zakat and what not?
Certainly most of these things are predefined in the sunnah and some in the Qur'an. But why for example is there no application of qiyas in cases such as platinum or diamonds which both are also considered as wealth and some may even consider platinum as the new "gold".
I know that for a person who is earning from selling these would need to pay zakat so these kinds of examples should be excluded as indirect Zakat on these items.
Maybe a better formulation of my question is:
Why some kinds of wealth are due for zakat while others are not? And to what extent can some become a due via analogy (qiyas)?