Most people believe that Valve has forgotten about Half-Life 3 and at this point, there is not going to be a third installment for the franchise but why is it so?
Knowing how big the fanbase of the Half-Life franchise, you would think that Valve will be taking advantage of that and quickly put out another Half-Life game but clearly, it is not the case.
Things have changed a lot since Valve made the last Half-Life game and at the end of the day, and while Half-Life was a huge part of Valve at the beginning, Valve had other things to focus on when it was time to created the third installment.
Valve has made it very clear that they would only work on games that they are interested in making so it is also possible that after the long break, nobody in Valve was actually interested in exploring the possibility of the game anymore.
We also know that Valve did take a break to work on their engine. Now that that is done, we might see more games from Valve but whether or not it is going to be a Half-Life game, well, we will have to wait and see.