Looking at Valve list of games, there is a common pattern that is not difficult to spot. It seems that the game developer prefers to hop from one AAA title to another. It was first seen with the announcement of Portal 2. Following its release, Valve went on to announce Counter Strike 2 before Dota 2.
It is obvious that Valve wishes all its AAA games to stand on the same platform by having a sequel each. All that is left is Ricochet 2 and Day of Defeat 2. Once the cycle is completed, Valve might just head on to complete a trilogy for all its games.
Then there is the Source 2. It is no secret that the game engine is being developed and the timing of it fits perfectly to the sequel process. At the rate it is going, Source 2 looks to complete after the development of Day of Defeat 2 is done.
Another thing to consider is with the current gaming age. 2014 will be the year where gamers transit to the next-gen games. If Half Life 3 is going to come out, it is going to arrive on the next-gen.
Put these three variables together and everything will make sense. It might be too hard to swallow with all the false theories going around in the past but this theory is something that Half Life fans should look forward too. After all, it is for the sake of Half Life 3.