Why does mixing inks make subractive colors? I have little knowledge of color theory and chemistery. Recently I came to know that printers use CMYK colored inks and combine them in different proportions to achieve any color on print.  

Let us suppose I fill white paper fully with red sketch then white light will fall on inked surface and all colors(wavelengths) except red will be absorbed and only red will be emitted/reflected. Good. Now I overfill that paper with green sketch. Now two things can happen:  


Both the inks of sketches mix but do not interact molecully. Like two chemicals A and B mixed in water and both A and B are everywhere in water but they are still distinct molecules. A's and B's molecules don't react chemically.  
Both the inks of sketches mix and interact molecuelly. Like HCL and Na2SO4 are mixed in water and they react molecually to make h2SO4 and NaCl.  


Now if 1 is true then on any point on paper's surface I have two types of molecules, 1. that reflect red light and 2. that reflect green light. So when white light will fall on paper then from every point two colors will be reflected, red and green. When they'll reach someone's eye then the perceived color will be red+green = yellow. So inks should make additive color.

On the other hand if 2 is true then molecules of red and green ink will react chemically to make a new kind of compound. Now it is not necessary that the new kind of compound absorbs both red and green. It could emit/reflect any random color. So the paper could be of any color depending upon the chemical formula of inks used. So in this case too inks don't make subtractive colors.

Sadly in reality inks make subtractive color and the color of paper actually is dark brownish black not bright yellow. So in reality the mixed ink absorbs almost all colors including red and green which were remaining.

So my question is why does both red and green got subtracted from the mixed ink? In general why does mixture of inks produce subtractive color rather than additive?
The issue is that you're thinking about inks reflecting color, when in reality you should be thinking about the inks absorbing colors.

If the function of inks were to reflect colors, then by adding more and more ink (of a single color) you'd be able to make brighter and brighter colors, as more ink means more reflection. Instead, it's the white paper (rather than the ink) that's reflecting the light, and more and more ink (even of a single color) makes things darker because more and more light is being absorbed.

That's why mixing pigments/inks is a subtractive process - as you add inks, you increase the amount of light that's being absorbed.

So let's go to your example. Let's simplify things by considering only three wavelenghts of light: red, green and blue. Your red ink absorbs the green and blue light, whereas the green ink absorbs the red and blue light. Thus when you mix the two, each absorbs the light it would in isolation, and you have very small amount of blue light, and also very little red or green light, leaving you with a very dark, perhaps slightly yellowish-brown color.

Now consider subtractive inks. You have yellow ink, which absorbs just the blue light and you have magenta ink, which absorbs just the green light. You mix the two together, and the magenta ink absorbs the green light, the yellow ink absorbs the blue light, and the red light is free to be reflected, resulting in a red colored piece of paper from Y+M.

Generally speaking, modern inks (at least the standard, non-color changing variety) involve no chemical reactions in color production: mixing inks and pigments is solely a physical change based on absorption of light.