I think the fed is worried about what happens when the interest rate hits zerio and they cannot lower it anymore.
There are already people warning about a carry trade being considered against the USD if it's interest rate drops. That could trigger a large run on the dollar and set off a new crisis.
Also, I was reading about the interest and currency derivatives banks have. There's like hundreds of trillions worth of insurance against currency and interest rate swings.(See other thread). If that's true and they get called it could collapse something, possibly overseas. Who really knows.
As the fed gets closer to zero it's gun is running out of bullets for these failures. I think right now it's saving ammunition for the next bank failure.
I don't think they care about inflation right now, though obviously that's a problem too. Remember everytime the USD drops, oil spikes and airlines get closer to folding.
// edit
Airlines etc matter for banking because they're barely above water, inefficiently structured, getting swallowed alive by costs and a lack of ability to raise costs without further losing customers. They're also heavily debt laden. They not only owe billions to banks that are desperate for cash, but the banks probably have credit derivative (insurance) on default of those loans. Which means if an airline can't pay or goes bankrupt, a bank is going to take both a loan write off and default insurance losses in the billions, and be looking at the airline like maybe it wants to liquidate it.
NWA doesn't like $105 oil
If they're complaining about 105 oil imagine when it hits 120+.