Catherine O'Hara's Gail, who serves as Jackson's resident therapist, hasn't been the same since Eugene's death. Still, she continues seeing clients, including Joel, who she still carries resentment towards based on what happened to Eugene. Season 2's sixth episode finally explains the details surrounding Eugene's death and why Gail has those issues with Joel. It also helps explain why Gail is so tuned into Ellie and Joel's complicated relationship when she meets with Ellie following Joel's death, seeing as she has witnessed several of their fights firsthand.
Why Joel Killed Eugene In The Last Of Us Season 2, Episode 6
Eugene Was Going To Die Whether Joel Killed Him Or Not
During The Last of Us season 2's fifth flashback sequence in episode 6, Joel takes Ellie on her first official patrol. She had been begging to join the crew for years now, but Joel was adamant that she had to wait until she was older. The day comes when Ellie turns 19, when Joel accompanies her on one of the safer trails to show her the ropes. During the patrol run, Joel and Ellie are alerted to Eugene and his partner needing backup due to an infected attack. As viewers know, the outcome isn't good for Eugene.
Ellie is hesitant about the plan, but Joel promises that he will stay with Eugene until she meets back up with them with their horses. However, Joel doesn't intend to keep the promise because he leads Eugene to a scenic ledge to kill the man. The man begs to see his wife again, as Joel counters that "if you love someone, you can always see their face." Knowing there's no way to save him or get him back to Jackson in time, Joel shoots and kills Eugene before he becomes one of the infected.
Joel Lying About Eugene's Death Justifies Gail's Behavior During Joel's Therapy Session
Gail Had The Right To Be Upset With Joel
...it's surprising that Gail would even agree to see and talk with Joel after discovering what really happened during Eugene's death.
Gail is already inconsolable, so when she learns what really happened to Eugene, she becomes extra distraught and even slaps Joel. Following that encounter, it makes perfect sense why Gail wouldn't completely trust Joel during their therapy sessions. In fact, it's surprising that Gail would even agree to see and talk with Joel after discovering what really happened during Eugene's death. The man was never going to live, but Joel didn't handle the situation in the best way.
Did Joel Do The Right Thing By Killing Eugene?
Joel's Lies Caught Up To Him This Time

As speculated earlier in The Last of Us season 2, Joel doesn't have much of a choice when it comes to killing Eugene. The man was bitten and unless the show plans to copy Ellie's immunity reveal, death is the only outcome. If it wasn't for Joel, someone would have had to kill Eugene shortly after the tragic twist. So, in the end, Joel does what needs to be done with Eugene, especially when it comes to putting anyone else in danger, even Gail. Joel's approach to the matter, however, could have been better.
For one thing, Joel should never have promised Ellie that they could bring Eugene back to fulfill his wishes to see Gail one last time. There is already tension between Joel and Ellie at this point in The Last of Us, and Joel's decision to lie to her only worsens the trust between them. Lying to Gail makes sense to a point, seeing as he's trying to protect the woman from more pain, but unless he was absolutely sure Ellie would follow his version of the story, he should've kept the details to a minimum.