Often a tap breaks because it is being bent.
There are ways to avoid this.
The hole should be the correct size for the thread being cut. If in doubt, a tiny bit oversize is safer than undersize. Zeus Charts give the correct size drill to use, and the nearest stick size, for this reason.
A very slightly oversize drill will mot decrease the % thread engagement ruinously.
The simple way is to make and use a Tap guide. Just a piece of metal drilled and tapped with the thread to be cut in the work, so that the tap is held square to the surface of the work.
If a hole has to be tapped in an inclined surface, a flat surface (such a spot face ) on which the drill and Tap can be used.
Use a Tapping Fixture (Mine is based on a stand for a pistol drill, but with the tap being held in a small drill chuck, and rotated by a short tommy bar.
In a lathe, Taps and Dies held in holders which slides on an arbor held in the Tailstock. In this way the Tap or Die is on the axis of the lathe, and the newly cut thread is subjected to the mimimum load, rather than trying to drag a Tailstock along the bed.
In a Mill My preference is for a spring loaded holder to guide the outer end of the Tap, whilst it is driven by a suitable sizes tap Wrench.
Suitably lubricated, backed off every half turn, and kept clear of swarf, breakage should be a are occurrence.
Trefolex, Rocol RTD are suitable lubricants for Tapping. Bacon fat will also suffice, if the need arises.
Obviously when using a Die the workpiece should be he correct size for the thread being cut.
HTH
Howard