Can't reduce size of textarea in Chrome and Opera
Google Chrome has a some kind of restriction to show content properly to user. Because of that they edited the default actions of resizing on <textarea>. In older versions of chrome there was no restriction.
So if you use height min-height will be your height. So you need to set min-height and max-height only. Height overrides min-height in Chrome.
Here is a simple fiddle: http://jsfiddle.net/gAr72/1/
Edit:
You can see Firefox will work same as Chrome in this fiddle. Height is risky for design btw. Unlimited resizing always breaks the design. So limiting height and width is good option.