It boils down to one simple fact:
Half-Life, as a series, is worth more as an undefined concept than an announced project.
What do I mean by that? I mean that Valve will make more money off Half-Life games, and their games in general, if speculation continues. They get a humongous amount of free advertising, just from people talking about their games; even ones which may or may not exist!
A lot of people make the argument "if they're not working on it, nobody is going to be angry, so just let us know since we've been waiting so long!"
But that doesn't make any business sense. If you type in "half life" into Google search right now, here's what you get:
Bottom row is games, left column is number of search results. Here we can see that... people who use Google really love Left 4 Dead. Uhm... look I'm not one for normally throwing out values that go against point, so I'm gonna briefly explain this. I am taking into account that Left 4 Dead is one of the core Valve IPs. Portal didn't make it on here becaues as a search term, "Portal" is pretty much the most ambiguous thing on the Internet. Left 4 Dead may have small problems of that, but I think it probably is just that popular.
We can also see that later releases in the series are less popular than the original release, though that may just be a result of search term branding. So in the interest of fairness, I put quotes around all these results to see what happened.
So what does this mean? Valve is getting around 1 000 000 results for Half Life 3, even though it doesn't exist. Episode 1, which people didn't like as much as Episode 2, has less hits than Episode 2. The episodes also have less hits in general. What does that mean? I guess it means they aren't as popular, but I think it really just means that Half Life and Half Life 2 really stood out. Now, if they aren't working on Half Life 3, what happens then?
All those people who are constantly looking for info on Half Life 3 will stop searching. Some percentage of those searchers probably get back to Steam, and it's really just more company publicity. Revealing the lack of Half Life 3 would only remove free advertising for them, so why do that?
And if they are working on Half Life 3? Why not just tell us then?
Because last time they talked about a Half Life title heavily in advance, it did not end well.
And either way, they're getting tons of advertising. So might as well keep at it. Speaking of which, looks like I did exactly what Valve wanted. I talked about Half Life 3.
(Bonus points if you noticed I stopped using a hyphen.)