It looks to me like a couple of things going on.
Number one, a glass hard drill bit. Too hard (glass hard), or too soft of a drill bit is kind of a common thing in the cheapies. Some do work OK, but there's a very high occurance of what I believe to be heat treat failures. I've never had a broken drill bit look like that, but any time I've had one shatter that far along the flute (not a flute, opposite of flute... The only way that you couldn't brake a drill bit if you tried...), any time I've decided to science that, I've never had one fail to fail the hammer test. Set it on an anvil (even the back of a vice is an adequate anvil), and smack it with a hammer. You could break about any good drill bit, but if a good sharp hammer blow literally shatters the drill.... I'd bet yours would fail that test too. Then you know that that set isn't a candidate to drill important things with, unless you're OK with having half of a drill bit as a permanent feature of that project.
Number two, I'm looking at the cutting edge. I could be wrong, but it looks "normally" sharpened. Bronze, like brass, kind of likes little to no rake on the cutting edge. Otherwise the drilll wants to "thread" into the work. Not as bad as brass, but same idea. It leads to chatter, grabbyness, and general displeasure during the operation. Although a quality drill bit will usually get the job done as is.
Number three, and this might very well be situational, with technique, drill grind ("brassed" drills or regularly sharpened drills), but I have a lot better luck drilling a smaller pilot hole. Just enough to comfortably clear the web, and thereby engaging more of the cutting edges on the final size drill bit.