The definition of "sport" is a fuzzy one. Some people will tell you that for instance darts isn't a sport because it requires no physical fitness and it's not competitive in that your performance doesn't effect the performance of the other person directly (in, say, football you're directly competing, in darts, golf and bowling you're both basically playing separately and then comparing scores)
If you want to write your paper on paintball and think you'll have to justify it as a sport, you can either point out that it's referred to as a sport by organisations like the
United Kingdom Paintball Sport Federation or say it fits into a dictionary definition of sport
QUOTE said:
sport
a. Physical activity that is governed by a set of rules or customs and often engaged in competitively.
b. A particular form of this activity.
2. An activity involving physical exertion and skill that is governed by a set of rules or customs and often undertaken competitively.
3. An active pastime; recreation.
I don't think you can argue it's not a sport under those definitions, but hey your teacher might be a hardass. You could always ask (unless it's due in tomorrow!)