Welcome to Fluther.
For myself, one of my primary motivations to participate in debate, discussion and essay (such as this, for a simple example) is self-interest: to help to clarify and crystallize my thought processes and reasoning for my own benefit. It also helps to improve my writing (hey, if you think this is bad writing, you should have seen where I started from).
I also have a modestly altruistic motive: to leave a record for posterity. (That is, because most of my attempts in this realm are in written form.) When I have experience, information or superior reasoning that can help others, and if I can afford the time and slight aggravation involved, then I enjoy leaving the nuggets for others to find. I also don’t like leaving the field to those whom I know to be incorrect, inexperienced or fraudulent, so that those are the only words left.
Less frequently, the person that I may be trying to correct – if I do have that aim – is because of a personal connection with the individual, and my wish that they not come a cropper or take a fall over bad reasoning, being misled by false, fraudulent or simply incorrect information – or even to test my own knowledge. I do not believe myself to be infallible. Sometimes my argument helps me to discover the error in my own facts, logic or belief. But not often. I am pretty damn incredible, after all.