Facebook didn't make $3.7 Billion last year. That was their total revenue.
As for going public, there are a number of reasons. For one, it allows a company to raise capital without taking on debt - capital that can be used to build on what their doing. Mark Zuckerberg has been clear in that his main motivation right now is to continue to evolve Facebook into a powerful social resource, rather than to make lots of money. In his words: "Simply put: we don’t build services to make money; we make money to build better services." And raising more money gives Facebook more ability and flexibility to do that.
For another, some people that currently own Facebook stock likely want to monetize some of that 'on-paper' wealth at some point. The stock being publicly traded enhances their ability to do that, likely at rates more favorable to them than they would get through private sales. One reason for going public now might relate to uncertainty with regard to the extension of lower capital gains tax rates beyond 2012. If they go public before the middle of this year, the 6 month window during which at least some current shareholders can't sell their shares will expire before the end of the year. So, they might be able to pay a lower tax rate on the money they make than they would if they couldn't sell this year and rates go up next year.
We should be clear though, only a small portion of Facebook will be sold in this initial public offering - maybe 5 or 10%. The people that now own Facebook will still, for the most part, own Facebook. And Mr. Zuckerberg will maintain essentially complete control of the company and important decisions because of the number and class of shares he owns, the voting rights those respective classes of shares are entitled to, and the irrevocable proxy he holds with regard to the voting rights of certain shares that are owned by certain other people. Facebook will remain, for practical purposes, Mr. Zuckerberg's company, and anyone investing in it should be aware of that.