Why is a transit of Venus so rare?
If Venus and the earth orbited the sun in the same plane as the sun, transits would happen frequently. However, the orbit of Venus is inclined to the orbit of earth, so when Venus passes between the sun and the earth every 1.6 years, Venus usually is a little bit above or a little bit below the sun, invisible in the sun’s glare.
A similar thing happens with our moon. Every month the moon passes between the sun and the earth, yet we do not see a solar eclipse every month. That’s because the moon’s orbit is also slightly inclined to earth’s orbit, so the new moon is usually a little above or a little below the sun. The transit of Venus is essentially an annular eclipse of the sun by Venus.
See the paper plate activity at http://transitofvenus.nl/wp/2012/02/16/pattern-on-a-paper-plate/ for a model that shows the transit frequency visually. Or watch the video Predicting a Transit of Venus: The Two-Minute Explanation . A Sky & Telescope article Transits of Venus Explained also delves into the celestial pattern.