Biologically we prefer people most like ourselves. To live in long term bliss, opposites don't attract- they repel one another. It is just easier to share space with someone who agrees with you, likes what you like, and has similar values and preferences.
However, the best person especially in business is the one who will do everything he can to prove you wrong. Instead of sitting back and getting comfortable with what your do and how you do it, this person will be the thorn in your side and annoy you until you question yourself and try something different.
In workplaces, similar personalities tend to gel together. They chose the same shifts, volunteer to work on the same projects and even do similar job functions. They are more alike than different in very fundamental ways. Positive people tend to be a magnetic force to each other. Extroverts tend to befriend other extroverts and naysayers tend to side with other pessimists.
However, more productive collaborations would pair opposites at work. A progressive leader would throw together analytic types with the more social, bigger picture visionary thinkers. The Visionaries would at first be slowed down by the annoying details, stark reality and research the analytics provide. However, long term the collaboration provides just enough tension to work.
Although annoying, opposite personalities do balance our perspective and cause us to see different potential outcomes. What we need to do is understand, appreciate and respect each other for our differences and work for the good of the group. One persons strength can become another persons axe to grind because we don't know how to value those qualities that we don't personally possess.
A directing personality may be seen as controlling and overwhelming when really their timelines and deadlines keep things on track.
A hard working person who also shys away from change and conflict persistantly gets the job done.
Instead of recognizing our differences we get embroiled in arguements that we don't know how to manage. As a result we fall back into our comfort zone and stick to the people we know and like.
Pick the person least like you and spend the day with him and see where it goes.