Hi oldsoul,
I'll try and answer this for you. The simple reason is that Cancer and Aries are separated by 90 degrees - an angle which is called a square in Astrology. Squares produce tension, and something of a 'crossed purposes' situation. Extending this to your friend the simple answer is that you and he are likely to find yourselves at cross purposes or easily generate tension between you.
BUT things are never that simple - as you point out from your post. Firstly tension and a build up of energy can actually be a stimulus to getting things done - squares can be very constructive if handled properly.
more importantly though, you and your best friend are not simply Aries and Cancer. When asked what sign they are people give their Sun sign but this is not the only sign in our horoscopes - we each have all twelve, though the blend of these and the emphasis on them varies according to planetary placements and the time that we were born.
Its quite possible that either you have a signifcant amout of Cancer in your chart or other Water or Earth signs, or that he has a significant amount of Aries or other Fire or Air signs. So you may well be extremely compatible in Astrological terms.
Actually apart from sun sign columns in papers, Astrologers are not that general at all and like to look very carefully at all the planets and signs and where they lie in your chart before committing themselves. Indeed many professional astrologers do not like Sun sign columns because they are not sufficiently serious. That may be an over reaction but Astrology is not what you read in 'Your Stars for the Week' columns.
Finally, Astrology is not fate - its quite possible, even with no indication in their charts, for two people to get on really well together. If you work at your friendship and both of you are quite happy to put effort into maintaining it, then it will work despite any astrological obstacles. The Astrology simply gives you an indication of what obstacles, or goodies lie in the path of your relationship. Make use of the goodies and avoid the obstacles and all should be well