Why does my ice do this?
I have heavy plastic ice cube trays that came with my refrigerator. I flex them to get the cubes to pop up enough so that I can flip them out into my glass.
Sometimes, but not always, the cubes shatter and instead of having a big cube, I get a bunch of tiny little ice pieces. Why does this happen?
I noticed that happening, too. Try letting the tray dry completely before refilling it. Also, my parents finally got new trays after a number of years and that solved their problem.
It's silly, but I get bugged by that too. ;) Just as nemo said, it helps if the trays are dry. If you have shards of ice in the bottoms of the trays (which can build up in increments over time), broken ice is very likely. But instead of drying the trays between fills, you can just rinse them, turn them upside-down, and give them a good whack on the edge of the sink to get the particles out, and then refill.
"the cubes shatter and instead of having a big cube"
Ice cubes were formed with too many fractures. In other words, the ice cubes were already broken.
You probably just need to replace the trays. When ice trays develop pocks from regular wear, the ice starts to form in the rough little fissures as well. When you go to crack the ice out of the tray, it shatters rather than popping out. I don't think you can find a way to polish the roughness out, so your only choice is to get new trays.