Why do they consider radioactive matter with long half lives more dangerous than matter with a short half life?
A more balanced approach might be to recognize that both short and long half-live materials can be serious hazards, but usually for somewhat different reasons. Also, the devil is very much in the details here, because issues such as how your body absorbs the isotopes is also very, very important.
Radioisotopes with short half-lives are dangerous for the straightforward reason that they can dose you very heavily (and fatally) in a short time. Such isotopes have been the main causes of radiation poisoning and death after above-ground explosions of nuclear weapons.
Iodine is an example where preferential absorption by the human body can further aggravate the dangers of short-lived isotopes.
Long-term isotopes are more complicated. They don't dose as heavily, but there are a lot more issues than just that. Plutonium for example is comparatively long-lived, but some of its decay products can be quite nasty. Also, plutonium happens to be particularly toxic due to its chemistry, which aggravates the damage it can do.
The biggest danger from radioisotopes with mid-to-long half lives is that they can keep an entire region of earth nastily radioactive for a very long time, e.g. hundreds or thousands or even tens of thousand of years. That's the main reason why disposing of reactor wastes, which often contain just such isotopes, is such a contentious issue.
At the extreme end are isotopes that are so long-lived that their hazard levels are close to zero. Uranium-238, the kind left after the fissile 235 is removed, pretty well falls into this category. Bismuth (as in the main ingredient in a popular pink stomach relief aid) is ironically in this category, with a half-life so long it's hard even to tell that it is radioactive.
why is plutonium considered more dangerous than radioactive iodine?
Because the press have heard of Plutonium and Pu=atomic bombs=bad
Plutonium's danger is over stated, it's insoluble so hard to get into the food chain and even if ingested is going to go straight through you. Pu is only a real concern if breathed into the lungs as a fine dust.
Iodine is much more of a concern to human (and animal) health it is readily absorbed in the body and is sufficiently active to have serious radiological effects. The only good thing about Iodine is that if it occurs in a reactor accident on the other side of the world and takes 8days to get to you - there is only half as much of it left.
Half life is defined as
the period of time it takes for a substance undergoing decay to decrease by half. The name was originally used to describe a characteristic of unstable atoms (radioactive decay), but it may apply to any quantity which follows a set-rate decay.
The shorter the life time the faster the material returns to normal levels of radioactivity.
Iodine in eight days exudes half the radiation it had the first day. In sixteen days it is 1/(2*2)=1/4 etc.
Plutonium takes hundreds of years to get to halve its radiation level.
In addition the danger of the body replacing its minerals with radioactive ones is a major factor of danger from long lived elements, like plutonium, through the food chain, from fallout and ground pollution. The shorter the lifetime , the better.