First separate science from TSA policy....
Oxidation is the removal of an electron from a reducing agent. Often this releases energy, sometimes setting things on fire, or with a good mixture, exploding.
You cannot take *certain* oxidizing agents on an airplane, mostly the ones that have a history of being used for no-no purposes. But whether something is an oxidizing agent depends on the strength of the reducing agent, ie water can be an oxidizing agent with stuff like LiAlH4 or Na, making blanket bans(by regulators that cannot tell sodium chloride apart from semtex) on oxidizing agents as silly as the nudie-scanners.