I understand that drum sticks are supposed to be hit with the tip, and the only reason you hit the drum set with the shaft is to do a rim shot- so technically it would take a lot of rim shots to break a drum stick.
How does a drumstick break then?
As any material, wood/plastic/carbon fiber will become more and more breakable when they take some damages. You don't only hit the drum with the shaft when you do a rimshot. On cymbals (crash or charleston), you can have differents sounds by hitting with the different parts of the drumstick. If your stick is already weakened, then sometimes even one little hit can be enough to cut it in two.
Keep in mind that when you are playing, sometimes you are so much concerned by your music that you forget how strong you can be and how loud you can play :) That's usually how I break drumsticks, playing some songs I love in live, or doing solos.
At the end of the day its all down to technique and placement. You can always expect to hit the bladed side of cymbals when the swing up and down from hits which acts as an axe to cut through your sticks gradually. If you are playing metal for example that is a lot of hits in a short space of time. Its wood verses metal the sick will lose.
The best way to prevent a stick from breaking is to make sure the contact is flat surface to surface on cymbals and try avoiding hitting the rims of drums during fills and progressions. because I tend to find I hit toms and snares heavier than symbols. One heavy rim shot can break a stick.
I also noticed that its mostly my hi-hat stick that wears quicker (in my case right handed would lead on the HH. Obviously it's swapped for lefties).
Drumsticks are not designed to take impacts over a small surface area. (that is, all of the force of your strike placed either at the tip, or along the shaft of the stick)
Good drumming ergonomics require the proper setup of your drums and cymbals. Toms and the snare should be positioned so that the drums make contact with a large surface area of the stick. Listen to what your rack toms sound like when you hit them first with only the tip, then hit them with as much of the stick, still getting a center-hit.
The cymbals are the same way. They should be tilted slightly toward you, and it should be easy for you to strike the lathed edge across the cymbal, instead of hitting it dead-on.
To say these hits are the only ones you should make with your set is foolish. The entire stick should be used. And you will have passages in music where bashing is a requirement. But bashing straight on and down shouldn't be your only mode. Unless you like buying a lot of sticks.