Why do some element symbols have one letter while others have two?

There are over a hundred different elements, so there simply aren't enough letters in the alphabet to give each element a one-letter symbol.

Also, the symbols are abbreviations of the elements' names, sort of. For most elements that's obvious. However, some elements have English names that are quite different from Latin names (e.g. Sodium is abbreviated Na, which stands for Natrium - same thing, different language).

There are also some elements which share the first two letters of their name, e.g. Magnesium (Mg) and Manganese (Mn). Obviously, both couldn't be abbreviated Ma, so the people who made the abbreviations got creative and skipped a letter. Similarly, the postal abbreviation for Maine is ME, which doesn't make a whole lot of sense - but MA is Massachusetts, MI is Michigan, and MN is Minnesota, so Maine got stuck with ME.
26 letters of the alphabet
more than 90 elements

you do the math...
Because there are only 26 letters in the alphabet.
Because there are only 26 letters and over 104 elements.
Generally the ones with one letter like carbon (C) or hydrogen (H) got in first by being discovered earlier. Also more common elements tend to have 1 letter.
There are only 26 letters in the alphabet, so many elements are given 2 letters because there are more than 26. Watch for 3 letter symbols when we get over 100 elements.
It's arbitrary. As has been said, the elements that were discovered earlier, and the more common elements (which usually coincide) get the single letters, and the less common ones that get discovered later get 2 letters. Of course, there are those that are yet to be named that have 3 letters based on the atomic number, so, it really has no significance. Some elemental names that we use in English are very different than those from Latin, such as Iron was called ferrum in Latin. If you were to abbreviate "ferrum," would you use F, or Fe? It's really all about the preference of who gets to name the element on the periodic table.
There's an interesting story about niobium (Ni). For quite a while, there was a rift between the metallurgists who called it Columbium (Cb) and the chemists, who finally won out. But you may stray across the alternative name.

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