I'm sure that we can trace the order of letters in the modern Latin alphabet to precursors (the Greek alphabet, various Semitic writing systems). But at some point an order had to be chosen for letters without reference to a predecessor, since none existed. What determined the order of letters at that point? Was an order chosen arbitrarily?
Alphabets in general tend to be arbitrarily arranged according to the idiosyncracies of their inventor. For example, cyrillic has its order due to arbitrary decisions by St. Cyril, the inventor of the cyrillic alphabet.
In some cases, a verbal mnemonic is used to arrange the letters. For example, in the old Gaelic alphabet, it was based on trees, the first stanza going beth, luis, fern, sail, nuin, "b" "l" "f" "s" "n", these trees being birch, rowan, alder, willow, ash. These trees all go together, because they grow in the same kind of places (wet areas).
This may have been true at one time for Phoenician, but whatever the rationale once was, has been lost.