Question

why are radicals so reactive

Answer 1

They have a charge as a whole on them.
Let's put it simply.
H has valency of +1 and O of -2.
If there is a combination or decomposition of these from any substance and if they combine.
The valency on the compound remains -1.
Hence the radicals are so reactive.
These were just the bare bones. If you need a detailed analysis, just ask.