The clutch has a lot to do with it, but it's also the construction of the internal gears/syncros, and a manual transmission model also usually has higher ratio gears in the differential vs. automatics that sometimes come with low optional gears like a 4.10 that give even higher towing capacity.
There's also the CYA aspect to it, sure. A lot of people in vehicles with a manual trans would haul 3 tons in 5th gear at 70mph on the highway if the towing capacity on paper was 3 tons.
That said, the engineers do know what they are doing - the towing capacity is what it can tow safely and reliably around the country, not the absolute maximum towing capacity no matter what. You can "tow" well over rated capacity with a manual if you're just pulling something a short distance at low speed and stick to the low gears.
You aren't going to get away with towing a 4400lb car/trailer combo thousands of miles on the interstate when the towing capacity is 2400lb.
It WILL pull it initially, since the 4.0L with an auto will pull it, but you risk severe transmission/drivetrain damage along the way. It will be quite unpleasant to have the vehicle come to a screeching halt or coast to a stop and be stuck wherever you happen to be, with a busted transmission AND a trailer. On the plus side, if your Firebird runs and drives, you have that to use.
If you want to tow a 3400lb car on a 1000lb trailer, you'll need an Explorer with an automatic transmission. Even better if it has the lower gears and the 5700lb tow rating so you have plenty of reserve capacity.