A few days ago, the YouTube channel "The Know" published a video talking about how Half-Life 3 was never getting made because they claimed that someone from Valve had tipped them off about the internal goings-on at the company and how "toxic gamer culture" had forced the company's hand into withdrawing resources and development from the title.
In the video, which you can see here, The Know's hosts stated that the company was afraid of "entitled" gamers and death threats, and had thought to reevaluate its stance on releasing Half-Life 3 after they saw the negative feedback BioWare received for botching Mass Effect 3's ending.
It's a quaint narrative, and it's probably untrue, but we'll never know because Valve doesn't want to say anything. The Know's Bruce Greene wrote an e-mail to Valve's Marc Laidlaw, who had various ways of saying "no comment" in response to his questions.
The tl;dr version of it is that Marc Laidlaw doesn't have anything official to disclose and that if anything were to go on record, it would be through a press release for all fans of the company to receive at the same time. Laidlaw said that any revelations about Half-Life 3 wouldn't come from a rambling series of e-mails and it wouldn't come from him, either—unless that would make a cool ARG, he joked.
You can see the full correspondence below.