Why is the central maximum the brightest?

A more physical way of restating Ron's answer: in diffraction theory you are adding up Huygens wavelets over the aperture with appropriate phase factors. The central fringe is the only one where the entire aperture is adding in phase, i.e. constructively. The next fringe will have 2/3 adding constructively and 1/3 destructively, then after that 3/5 - 2/5, etc. The farther out you go in fringes, the more of the aperture is just cancelling itself.

In single slit diffraction, assuming small diffraction angles, the intensity profile is the magnitude-squared of the Fourier transform of the function which is constant between -1 and 1 (up to units of length), and this Fourier transform is $\frac{\sin(x)}{x}$. This has a peak at zero, because of the falloff of $1/x$ but most importantly, and this can be seen qualitatively, the first zero of $\sin(x)$ is absent, the central maximum is twice as wide as all the others.