Why are fluoride ions (and ions in general) reactive?
Fluoride activity, or more properly danger, comes from the fact that formation of some salts of fluoride is energetically highly favorable for aforementioned metals. 

Calcium for instance, rather than in calcium carbonate, is more stable in $\ce{CaF2}$ form. Then, consequently, it will etch your bones eventually if there is a dermal contact with $\ce{HF}$. Other acids like sulfuric acid make a superficial effect and with a copious amount of water you mostly get rid of it. $\ce{HF},$ on the contrary, is a weak acid and slowly seeps through your epidermis to your bone.

$\ce{HF}$ is also reactive with glass, through silicon. It may also etch the beaker or any other container through time so you don't want to store $\ce{HF}$ for a long time in glass containers, actually same with bases to a lesser degree. 

$\ce{F}$ can even react with noble gases, you should just look at the last product and compare the overall stabilities of the current form and the final form. Fluoride simply more stable in $\ce{CaF2}$ solid than in solution.