I chimed in with my own thoughts in the comments section and pointed out some things that I think the other commenters may have been missing. Hopefully, it was helpful.

You make some good points:

For example, if I follow @CrossFit on Twitter, that's another way of expressing that I am interested in CrossFit. It's a subtle point, but in aggregate, hundreds of millions of people speaking their minds about all sorts of interests in real-time coupled with the ability to tap into these content streams presents some powerful opportunities for a wide variety of ventures ranging from the typical placement of advertisements to the less obvious studies in social sciences. (That's to the point of tapping into the collective intelligence of the network.)

Furthermore, whereas some other social platforms like Facebook or Google+ have various layers of privacy controls that govern the use of the data, Twitter's platform is fairly unrestricted and open, making it fairly trivial to tap into these "public" streams of interactions. In my opinion, this makes it a prime frontier for creating predictive analytics (such as sentiment analysis) for any applicable domain.

These make me wonder why Twitter wanted to be an advertising company instead of a data mining / analytics company.

The beauty of user-generated content at scale:

The best thing from investors’ point of view is that Twitter, like Facebook, is able to keep building a large audience with very little expenditure. Its users are creating the content, and Twitter just has to keep the servers running and make sure the interface is welcoming and try to avoid Fail Whales.

The good story is about network effects:

Twitter and Facebook command big chunks of their users’ time and attention — attention that they can sell advertising against — without the messy and expensive responsibilities of creating any content themselves. At The Washington Post, we have a big roomful of people paid to write articles we hope you will click on; a TV network has to spend millions creating shows that they hope you will watch.

Twitter and Facebook not only don’t have those burdens of producing content, but they have the added benefit of knowing exactly who their users are, and where they are. So the advertisements they do display are more precisely customized for what that particular user is interested in.

So that’s the bullish case for Twitter: Strong network effects, great economies of scale, sky is the limit.

Here’s the bearish case:

All that might be true, but the company hasn’t shown it can extract meaningful revenue (and profits) from those users. And the business of running a social network has proven astoundingly fickle, so there is little assurance Twitter will still be a thing a few years from now.