Your host, Y Combinator, strongly disagrees: http://www.paulgraham.com/growth.html
First two sentences in the linked article:
> A startup is a company designed to grow fast. Being newly founded does not in itself make a company a startup.
A successful startup in the eyes of VCs grows fast. It has to, so VCs have some hope of making a non-stupid return. Which is why we get all the drama around unicorns etc etc and more etc.
Does that mean that you, as a founder, have any obligation to play that game?
No. You. Do. Not.
If you choose not to, that's very much your choice. It gives you a number of advantages, including no loss of control over direction or everyday running, a very much lower danger of being fired from your own project, and a wider choice of potential investment sources when you've been running profitably for a while. (Are VCs the only money source in town? Not even close.)
And if you have a solid business model, it significantly raises your prospects of still having a business - and a job - when the unicorn hunter scene crashes and burns around you.
Which it inevitably will - possibly quite soon.
The disadvantage? If the business is seriously viable with many real customers and profits and such, you may to have to settle for being a multimillionaire instead of a billionaire.
Tough break.
I see the two forms of business sometimes differentiated in that way.
Startups are designed to go fast and cash out. The founders make a fortune and move on to something else, life doesn't really change for anyone else. A business with real longevity will go more slowly but everyone in the business will share in the ride.
The opposite kind of small business, to me, is the "organic" company which funds growth out of earnings.
This is quite aside from our like or dislike for startups.