You know who's infinitely patient, has read every psychology text book and is available immediately at 2am and not in a week that you have to schedule an appointment for? ChatGPT. (or Claude or any of them.)
A therapist does more than just listen. A therapist is more like a driving instructor sitting in the second seat that points out things that you should pay attention to, and can take the wheel if you head into dangerous territory.
If you say something like "I hate that people don't see the real me", LLMs would say "yes it's understandable that that would make you upset" basically confirming your reasoning as valid, while a therapist would ask "why do you want to people to see the real you?" or "What is in your words the difference between how people see you now, and how they would see you if they saw the 'real you'?". These kinds of questions force you to explain and identify your assumptions and reasoning.
LLMS are more like friends, providing a listening ear, but otherwise just nodding along.
edit: To be clear, this is why llms are NOT a good replacement for therapy. Using llms will likely only exacerbate instead of mitigate.