My reasoning: http://blog.planitwide.com/about/
To build something that could have lasting impact while solving a real problem in the world.
In my case I'd say it's a combination of a lot of different factors (some valid, some possibly bogus, whatever).
In no particular order:
→ Desire to have more control over my own fate / not have a "boss" in the conventional sense
→ Desire to build something bigger than myself
→ Desire to leave a legacy behind that would outlive me
→ Desire to change the world / improve people's lives by creating jobs, creating a place to work that reflects the values of the kind of place I'd want to work
→ Desire to be wealthy
→ Desire to prove doubters / critics wrong
→ Desire to build a great team and do fun things together
etc. It's hard to weight those and say which are most relevant compared to the others, but the "desire not to have a boss" is definitely up there, along with the fact that I just like building things (in this sense, I'm referring to "building" company).
And yes, before somebody says it, I know that "you always have a boss" in some regards. But a "boss" in a metaphorical sense, referring to "the board", "the market", "your customers", etc. is still qualitatively different than having one discrete individual, who has you under his/her thumb, and can yell "jump" while expecting you to say "how high" and who can fire you at will, and generally boss you around.
Trust me, if someone is starting a startup for himself the last thing he want is doing it to be like someone else. As for myself what inspired me is the desire to leave a mark in the world rather than being one of the billions who lives and dies and no one notices their existence except of their family.