Why aren't "radioactive items" allowed on flights?
Radioactive substances are potentially hazardous to people. 

It is correct that many radioactive items would be perfectly safe to carry onboard, e.g. a key hanger with an alpha or beta particle emitter cast in acrylic, or a radioactive source for scientific purpose, if that source is properly packaged.


Glowing key hanger containing tritium. Image source: Nite GlowRing

Travelers usually do not carry radioactive items with them. If there is the need or wish to bring a radioactive item along, there is normally no need to have it in the hand luggage. This makes radioactive items different from lithium ion batteries. While potentially hazardous, there is a strong demand for lithium ion batteries on board. Banning them would essentially ban mobile phones and laptops.

Airport security staff as well as airline ground and cabin crew are neither qualified nor equipped to inspect and judge the safety of radioactive items. Opening the safe packaging of radioactive items might be dangerous. An item that cannot be opened cannot be checked if something else is hidden inside.

Finally, radioactivity stirs an irrational fear in many (if not most) people.

Given the need to restrict the transport of radioactive material somehow, and the difficulties in controlling it in a more sophisticated manner, the ban of such material from hand luggage seems comprehensible.