Why CO2 is became a great solvent for Extraction in it's super critical region?

A fluid becomes supercritical when compressed by pressure & when its temperature is increased to greater value than that of its critical point. Although a supercritical fluid (SCF) is at single phase, it exhibits properties of both a liquid & a gas.

In this case, supercritical CO₂ has a relatively high liquid-like density. Solubility increases with density & pressure and also with an increase in temperature. Add to it that this substance has high absorption capacity in this state as well as low viscosity, and high ability for diffusion. All these factors render it more suitable for dissolving solutes.

In fact, because of the very unusual properties of supercritical fluids (low viscosity, low surface tension, high diffusivity, which result in wetting and penetrative properties), they can even be considered as a fourth state of matter. Pressure, not polarity, is a cardinal factor that determines the ability of a SCF to dissolve, and that ability can be controlled and varied by changing the pressure. Carbon dioxide is widely used as a SCF because it's easily and widely available, it's natural, cheap, inert, doesn't burn, etc. Take a look for example at McHugh and Krukonis, Supercritical Fluid Extraction, Butterworth-Heinemann, 1994.

Not sure what you meant by "react" - CO2 is not a very reactive compound. If you meant "behave" - you are right - even under supercritical conditions CO2 remains non-polar, although net polarity varies slightly with state conditions (pressure and temperature). It's considered a great solvent because of its tunability, which is the ability to vary solubility by changing pressure and/or temperature. Although with neat CO2 you will dissolve mainly non-polar compounds, you can still tune their solubility by changing the state conditions - which can become an useful tool for fractionation and recovery.