If I had to speculate based on what we’ve seen in the trailers so far, I would guess that Mark Russell lost a child to the Titans, either directly or indirectly.
The Russell family is at the center of Godzilla: King of the Monsters, with Mark Russell, Vera Farmiga’s Dr. Emma Russell and Millie Bobby Brown’s Madison Russell.
Kyle Chandler told Comicbook.com that the Titans have caused havoc with his family and he has suffered loss in the past that has fueled this hatred.