umm... perhaps this is obvious - but carbon steel is brittle, thus all
taps are "brittle" & in fact the cheaper the tap, the more likely it'll be a softer, lower grade steel & slightly more likely to bend before it snaps.
Trust me, I've broken my fair share of both cheapo ones & quality taps lol, it happens sometimes even with the best sets, good cutting fluid & technique (generally 1/4 to 1/2 turn out for every 1/2 to 1 turn in for aluminum) - nowadays I jus' borrow 'em from my buddy's 25pc Snap-On set... which cost $500 & breaks jus' the same - difference being free replacements ofc.
What the major problem really is (other'n dulling) with the cheap tap & die sets are irregularities, the threads they cut aren't nearly as clean & accurate as the quality ones, part of this is dulling but it's also due to the cutting edges being sloppy - they don't always line up with each other perfectly, making for oversized & sloppy threads - tap or die, same problems.
Still - I will say this, if it's a choice between a cheap set or no set at all... go ahead and get the cheapos as they are a pretty essential tool - but don't expect them to be great... & if you do spend the big bucks for the quality, don't expect them to be unbreakable - in fact, expect them to
break & use accordingly