Question: Is there a fallacy here, and how to respond to it?

I'll let the professional psychologists weigh in on this one, but I can see two distractions from two sides interfering in an
open honest communication between Liz and the seemingly ernest interlocutor named Sean. We're not given any information about
Phillip to really diagnose a particular trait other than the fact that he infuriates Liz and confounds Sean.

Liz's claim is a classic Argumentum ad baculum (See Dr. Bo's Appeal to Force) distraction i.e. "if Phillip keeps mistreating/misunderstanding or misbehaving this way I swear I will push the red button and destroy the frickin' world."

Appeal to Force
argumentum ad baculum

(also known as: argument to the cudgel, appeal to the stick)

Description: When force, coercion, or even a threat of force is used in place of a reason in an attempt to justify a conclusion.

Logical Form:

If you don’t accept X as true, I will hurt you.

Sean, The Inquirer. however, is also making an Appeal to pity or Argumentum ad Misericordium on Liz's behalf. There's no reason given for
Phillip's behavior or seeming lack of compassion or understanding. For all we know Liz is a drama queen, or, perhaps even a psychopath and Phillip's indifference could be simply one of either despair or sheer futility.

We don't know if he's called 911 or the suicide hot line or if he's in any way responsible for setting Liz off. Nonetheless, Sean, the Inquirer
makes an Appeal to Pity to all of us to intervene with Phillip on Liz's behalf.

Appeal to Pity
ad misericordiam

(also known as: appeal to sympathy)

Description: The attempt to distract from the truth of the conclusion by the use of pity.

Logical Forms:

Person 1 is accused of Y, but person 1 is pathetic.
Therefore, person 1 is innocent.

X is true because person 1 worked really hard at making X true.