Warning: Contains SPOILERS for Titans season 3, episode 3.
Red Hood claimed his first victim in Titans season 3's opening episodes, orchestrating the death of Hank Hall - here are the likely reasons why Jason Todd chose to target Hawk first. Played by Curran Walters and Alan Ritchson, respectively, Jason and Hank have (to varying degrees) been allies to the Titans since nearly the beginning. Following in the footsteps of Trigon (Seamus Dever) and Deathstroke (Esai Morales), however, Jason Todd was transformed into the team's most personal threat yet. After being killed by a largely unseen Joker in the Titans season 3 premiere, he soon returned as the dreaded Red Hood.
As Red Hood, Jason wasted little time and took over several criminal factions. Equally, he began antagonizing the Titans with psychotic puzzles — ultimately luring them into very public defeats. In Titans season 3, episode 3, "Hank & Dove," Red Hood took his twisted game to a new level. After capturing Hank, Jason had a bomb surgically embedded in his chest. As it counted down to the rhythm of Hank's heartbeats, the rest of the team floundered in their attempts to deal with the situation. Conner (Joshua Orpin) tried to manufacture a deactivation device, Dick Grayson a.k.a. Nightwing (Brenton Thwaites) sought to track Jason down, and Dawn Granger a.k.a. Dove (Minka Kelly) gave in to Red Hood's demands. Ultimately, every action was for naught, as Red Hood tricked Dove into pulling the trigger on Hank herself.
There are several thematic and tactical reasons why Jason chose to make Hank his first target. Firstly, Hank was predictably the Titan most gung-ho about simply putting Jason down. As such, Red Hood taking Hawk out of the equation immediately could be seen as merely a preemptive strike. Looking deeper, however, Jason could have been following a similar tactical plan as laid out by Deathstroke in Titans season 2. In the sophomore outing, Slade Wilson engineered situations to pinpoint the team's weakest link. In that case, it was the reckless Jason. Among Titans season 3's cast of characters, however, Jason had already used his experience to determine that Hank was now that person. He was the one that Red Hood could most easily manipulate into breaking away from the pack, especially since Hank was fresh from an argument with Dawn - which Jason could have eavesdropped.
Furthermore, Jason knew that Hank was the domino that could make all the others fall. As seen upon his arrival and the series of potentially final conversations, Hank was a truly beloved member of the Titans. As such, his dire jeopardy could singularly push several Titans to forgo acting rationally. That was especially true of Dove, who has possibly harmed the team's public standing all the more - first by openly committing robbery and then demonstrating her willingness to murder. Equally, now seemingly a criminal mastermind, the Red Hood version of Jason Todd would no doubt have figured that Hank's death could especially break the team in all the right ways. As a result, Jason may have set them up to be more easily manipulated themselves or simply prone to emotional mistakes.
Jason targeting Hank also tied into the deeper themes of Jason's journey and Titans season 3 in general. After all, Red Hood was described as Jason's attempt to conquer his fear. Killing Hank served as a thematic part of that. Hank was the Titan that most shared Jason's sensibilities. Both were hot-heads, prone to aggressive declarations and bravado. Both were, at their core, secretly soft-hearted and burdened by deep childhood traumas. Killing Hank could have been a metaphor for Jason exorcising one of his own weaknesses. Equally, tying into the theory that Jason Todd is also the new Scarecrow, the scheme forced Hank to confront his fear of being powerless and waiting for a rescue that'll never come. With Hank's death, the other Titans will now have to confront some of their own fears (and limitations). Given that Jason has long been plagued by such things, it already made for poetic revenge in Titans season 3.