1. No class except Wizard's have access to "named" spells.
2. Arcane Tricksters have access to Illusion and Enchantment magics. Bigby's spells are neither illusion nor enchantment spells.
3. Because an Arcane Trickster doesn't need access to a giant forceful/crushing/interposing/clobbering/"Hulk Smash" energy hand. Not their style.
I think that's enough reasons to reasonably understand why AT's do not gain access to them.
EDIT to add: #4. As cbjm points out, for those who like ["need"] mechanic/RAW explanations for things, Bigby's is a 5th level spell and ATs only receive up to 4th level slots. So there is, also, the literal reason that they can't learn it, regardless of flavor or spell school.