Well... the human-based carriers have large banks of lasers for ship to ship combat, among other anti-ship weapons... and on top of that, strike craft in SOASE are probably quite a lot larger than our own fighters (think about all the extra equipment you'd need to cram into a spaceborne fighter). The Vasari carrier cap has weapons too, and huge banks of nanites and probably stacks of random elements laying around ready to be assembled into something. Oh, and the TEC carrier has missile satelites it can deploy - I'm sure those take up quite a bit of room, too.
Modern carriers are really more dedicated to 'strikecraft' than that. I think the Nimitz carry like 90 or so planes... The Advent carrier cap carries 99 or some such, the Vasari one has only about 32, and the human one I think has 48? Well, that's when all are deployed... each carrier cap manages to replace it's losses somehow, so... I'm guessing they have spare strikecraft on board (or the materials to quickly assemble them).
16 squads for the advent is something like a full gross (144) of strikecraft. Hhhm, Vasari get shafted on the number of strikecraft they get... but that's another thread
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Edit: As for the Light Carriers... they used to only get 1 squad, so be happy that they got improved!