Michael,
Forgive me if I'm about to advise what you already know.
Steps to avoid breaking taps when using 'free hand':
a. Ensure that the tapping hole size is big enough for the intended thread:
b. Ensure that the tap starts square, either by sight against a visual (square) reference but preferably make a proper guide;
c. Always use a 'first' tap on tougher materials;
d. Use appropriate lubricant, ie proper tapping compound or neat cutting oil for steel, paraffin or similar for aluminium, dry for cast iron;
c. Back off a 1/4 turn for every forward turn;
d. For blind holes, remove the tap completely occasionally and, if possible, knock the debris from the hole and clean & relube the tap (I keep old tooth brushes for cleaning taps).
If a tap twists much in use it is clearly making hard work of the job and likely to break, so check (a) and (b).
Personally, I never pay the mark-up for HSS, on the basis that carbon taps are more than adequate for the amount of use they are likely to get in MY workshop.
Even following the above advise, you will still break the occasional tap; I think most of us do, even engineers that have been using them for years, which serves to highlight the use of carbon steel taps.
I hope that helps, if only to let you know that you are not alone.
Alan
Edited By AlanW on 21/03/2016 14:01:17