Why the letter "g" discrepancy between *giant* and *gigantic*?

Solution 1:

The word gigantic comes to English relatively recently. Giant, as you probably know if you've investigated the etymology, appears in Middle English by way of Old French geant [NOAD]. Gigantic, on the other hand, appears first in Modern English in the 16th or 17th century, three or four hundred years later. The reference at that time was probably to the original Latin (via Greek) gigas.

Solution 2:

One of those occasionally (but never perfectly) useful pronunciation rules for English spellings (which was not designed -- to be fair -- to represent Modern English pronunciation, but rather Middle English, quite a different-sounding language) is that C or G before I or E often get pronounced /s/ or /ʃ/ or /tʃ/ (for C), and /ʒ/ or /dʒ/ (for G).

This is a result of several historic bouts of Palatalization in both English and the Romance languages (notably French, which supplied loads of English words, and Italian, which supplied Latin words in the form of Church Latin, quite a different-sounding language from Classical Latin).

As the Wikipedia article points out, sounds around the palatal region (alveolars like /t/, /d/, and /s/, and velars like /k/ and /ɡ/), tend to "migrate" toward the palatal region in anticipation whenever the tongue moves toward that region, which is where tense front vowels (like /i/ and /e/) are produced (by the tongue, that is; other organs are also involved). It's a natural reflex, and is unavoidable at normal speech speeds. Everybody does it. So migration is more or less constant, though at different rates.

Of course, I and E are no longer pronounced /i/ and /e/ in Modern English, but the palatalization they wrought while they were both high front vowels lives after them.

That's all, really. Welcome to the wonderful world of English orthography. There's all these fossils lying around, which is fascinating for us paleontologists, but frustrating for tourists, who keep tripping over them.