Because transformations make everything so much simpler and your code so much cleaner.
Everything we draw on computers we describe with Cartesian coordinates (x, y, and maybe z). By a perfectly reasonable default, Processing uses one unit per pixel. When I’m drawing something, though, I don’t want to think in terms of pixels, but rather I would like to use whatever units are appropriate for the object I’m creating. If I’m drawing a house, I might use feet or meters. If it’s a face, I might use inches or millimeters. But then, if I’m drawing them together, I need to scale them into consistent units and scale those units to pixels. So I could include a scale factor in every single drawing call I make, but what a mess that makes of the code. Alternatively, I can just slap a scale( inches to feet conversion ); before my draw call and suddenly the face and house are in the consistent scaling.
Likewise, for convenience, I coded the face sitting about the origin so that I could easily use symmetry for the left and right, but now I want to position the face or even move it around. Again, I could litter my code with adding offsets to each individual draw call, OR I can just say pushMatrix(); translate( posx, posy ); drawFace(); popMatrix(); and leave the graphics calls clean and simple.
Nearly all of my Processing sketches start with
translate( width/2, height/2 );
scale( height/2.2 );
because that moves the origin to the center of the window and lets me draw a unit circle with a slight margin around it. Now I can draw stuff either in that circle or using sin/cos polar coordinates and I never have to worry about the screen resolution. If I want to crank the resolution high to print out a poster or make it small for an online GIF animation, my drawing commands needn’t worry about the difference.