Sounds to me like there was enough carbon the steel that it work hardened from the dull drill that was being forced into it and ended that fiasco.
I agree. There just isn't any way to work harden mild steel... so it probably wasn't really mild steel.
Or maybe not a consistent steel.
Someday I hope to find the perfect cutting and lubricating oil for use on my machine tools, but I guess it's confession time: I use whatever is handy as a drill lube.... Light oil, heavy oil, spit, antifreeze, water, candle wax, or even snow... & my drills seems to work just fine and last a long time.
Most of my old drill bit collection are Chicago-Latrobe HSS. They cut fine & sharpen well. Aluminum does tend to stick to the flutes... but for steel they are fine. For stainless steel caution is needed. But for SS, nothing beats very low speed, lots of pressure, a continuous chip, a waxy lube, and hopefully all with a brand new factory drill bit.
TIN coating is a good anti-stick for chips in the flutes....but I've not noticed it making any particular difference in drilling a hole.
A Drill Doctor is a marvelous tool and takes up a prominent place in my shop along with several well-sorted narrow boxes of drills awaiting attention. A kitchen tableware tray makes the perfect place to put drills waiting for attention. And wait they do; in fact in my shop they've been sitting there by the Drill Doctor waiting for years now.... Being lazy, I tend to just hand-sharpen a bit when I need it.
I will say this about the Drill Doctor..... if you are good enough to use one to advantage you are probably pretty good at sharpening generally. The DD does take some practice. Once figured out, it is better than hand-sharpening.
Lately it seems like more and more of my drills are ruined by poor chucking than by not being sharpened right. Or is it my less tight chucking - getting old now - or are chucks just not as good today?
Drill slowly with enough pressure to keep a chip forming. The lip should be cutting, not skidding.
rScotty