IdiomSite

I stumbled across a webpage with idioms, and it made me start to question how I would define some common English idioms. The webpage is IdiomSite.com, which features a banner across the top that defines idioms as 'a natural manner of speaking to a native speaker of a language.' My first issue with the page is with that definition--I feel the definition provides some kernel of truth, but there is a lot missing from how idioms are separated from other natural manners of speaking; also, notice the definition only includes a one-way relationship (in the definition, the listener is specified as a native speaker, but not necessarily the speaker of the idiom).

After scrolling down through the page, there are several idioms defined that I would argue with. The following three are examples of these potentially arguable definitions:

• 'as high as a kite': anything that is high up in the sky.
• 'barking up the wrong tree': a mistake made in something you are trying to achieve.
• 'chip on his shoulder': angry today about something that occured [sic] in the past.

My own uses of these idioms don't quite match up with the above definitions; however, I don't want to bias my audience. Do you agree with these definitions? If not, how would you change them to make them more accurate?