why not just 2 charts to make atlas for sphere? In http://en.wikipedia.org/wiki/Manifold_(mathematics)#Construction, it says that 6 charts can be used to make an atlas for a sphere. But the text shows that you have a chart for the northern hemisphere, and you can make a similar chart for the southern hemisphere. Hence, these two charts cover the entire sphere.
What am I doing wrong?
 A: The northern hemisphere and southern hemisphere don't cover the entire sphere. The sphere is 
$$\mathbb{S}^2=\{(x,y,z)\in\mathbb{R}^3\mid x^2+y^2+z^2=1\}.$$
The northern and southern hemispheres are, respectively,
$$\mathbb{S}_N^2=\{(x,y,z)\in\mathbb{S}^2\mid z>0\},\qquad\mathbb{S}_S^2=\{(x,y,z)\in\mathbb{S}^2\mid z<0\}.$$
These miss the equator $\{(x,y,z)\in\mathbb{S}^2\mid z=0\}$. Adding "east" and "west" hemispheres 
$$\mathbb{S}_W^2=\{(x,y,z)\in\mathbb{S}^2\mid x>0\},\qquad\mathbb{S}_E^2=\{(x,y,z)\in\mathbb{S}^2\mid x<0\}$$
still doesn't get everything: we are missing the points on the equator $(0,1,0)$ and $(0,-1,0)$. Finally, adding the last two hemispheres (east and west, only rotated 90 degrees) covers the entire sphere.

This raises the question, why are we defining our hemispheres with $>$ and $<$? Perhaps we could instead use $\leq $ and $\geq$, and this would let us cover the sphere with two hemispheres?
The answer is that a chart of a manifold needs to be a homeomorphism between an open subset of the manifold with an open subset of $\mathbb{R}^n$. The sets
$$\{(x,y,z)\in\mathbb{S}^2\mid z\geq 0\},\qquad\{(x,y,z)\in\mathbb{S}^2\mid z\leq 0\}$$
are not open in the topology of $\mathbb{S}^2$ (which is the subspace topology inherited from $\mathbb{R}^3$). So we can't use them as coordinate neighborhoods in the manifold structure of $\mathbb{S}^2$.

It does warrant mentioning, however, that we can cover the sphere using only two charts, via stereographic projection. The two open subsets of $\mathbb{S}^2$ acting as our coordinate domains are 
$$\mathbb{S}^2-\{(0,0,1)\},\qquad\mathbb{S}^2-\{(0,0,-1)\}$$
and for each, we project a line from the removed point to the plane, which one can check gives a continuous map. It is a tedious (but important) exercise to demonstrate that the smooth structure determined by stereographic projection is the same as that of the hemispheres (i.e., they are compatible atlases).
