Quoth Wolfram Alpha:
≈ 0.51 × lung air pressure that a typical adult human can exert (≈ 9800 Pa)
≈ 50 × sound pressure at the threshold of human pain (≈ 100 Pa)
And yet the news is not filled with stories of severe pain and ruptured eardrums from people puffing in each others' ears. With a 2 order-of-magnitude difference, it seems like even gentle breaths, waving hands to cool off, etc. should be sufficient to cause pain. What gives?
The interpretation of "lung air pressure" here is a little ambiguous, but if we assume that this means "the pressure difference an adult can produce by blowing on a membrane surrounded by air at 1 atmosphere" then the situation seems reasonably analogous to the tympanic membrane.
One obvious difference is that sound is a wave while blowing is a continuous stream. We can avoid this issue by changing them both to a single impulse, like a gunshot and a single puff of breath. This doesn't seem to make the problem go away. Wikipedia claims that 20 Pa is sufficient for "risk of instantaneous noise-induced hearing loss", and you can obviously exhale much harder than this even in a short breath.
I'm guessing the problem is in some misunderstanding of how I'm interpreting the physical quantities, but I'm not sure what that could be.