Iron kills a star because it is the first element in the periodic table that actually requires more energy to fuse, than it produces in the process.
Stellar cores are nuclear furnaces that, in loose terms 'burn', one element and produce 'ash' of a heavier element. Hydrogen turns to helium, helium to carbon (& some others). When four hydrogen atoms are fused into a single helium atom they use energy to do so. However once formed, they produce more energy than was required to slam them together. This extra energy can then be used to help fuse the next bunch of hydrogen. If you have a high enough starting temperature, and a high enough pressure, this allows for a self-sustaining fusion reaction.
Same goes for all the lighter elements, but the pressure & temperature requirements begin to rise, as each element heavier than the last requires more energy to fuse, and produces less energy once it's done.
Iron is the tipping point, it can be fused, but it actually uses more energy than it produces, which in effect COOLS the surrounding area, which slams the break on the reaction very, very hard.
The idea that stars cause iron formation in our blood is a bit off. I.e. a star blowing up nearby does not make iron appear in our blood, as the phrase suggests. Instead, all elements heavier than hydrogen or helium (And in truth most lithium) are created in stars and spread when they die. The vast majority are actually formed in the supernova explosions of supermassive stars. Oddly enough in those cases the heavy metals that build up in the core are NOT the metals that survive and spread. Those are completely annihilated in the explosion, and elements created as the explosion's shockwave causes fusion in the outer regions of the star are those that are spread out in the remaining debris cloud.
We are literally made of stardust, or even more aptly the ash from long dead stars.