It looks like you've learned something today. In the process, you've created a nifty little piece of art to stick on your shelf too.
But I must ask, despite my better judgement: Why were you attempting to use the "adapter" (tap wrench/handle) to drive the tap instead of just chucking in the drill?
Was it perhaps due to the tap slipping in the chuck? Your solution to put flats on the tap is certainly in my book of tricks as well - just not in chapter 1. If all other variables are fine, a drill chuck in good condition should hold even the very hard shank of a tap with enough force to cut threads without slipping.
I'll go out on a limb and make some general suggestions:
- Make sure the hole is drilled the correct size, or even a little bigger. Depending on material and your drill bit set, one or two sizes off can make a huge difference.
- Set up the job so that the tap remains square to the work. Difficult if you're using a hand drill, but if you brace your arms/elbows/wrists and try to create a 2 or 3 point support system for the drill you'll have a lot more luck and break few taps. If the tap binds, it's going to want to twist the drill out of your grasp. Much better to have a good hold rather than the drill twisting, moving off-square, and snapping off the tap. That said, sometimes its better to give firm support to the back of the drill and less on the handle. That way if it does bind it can rotate a bit on it's axis and save the tap from breakage.
- Use cutting oil. Other oils are perhaps better than nothing, but a true cutting (tapping) fluid can make a world of difference even on easy to tap materials. Not to mention prolonging the life of your taps.
.... or maybe you just needed a few more inches of length ... :P