Honesty really would be the best thing here in my opinion. Don't be embarrassed or ashamed to tell him. I had difficulty with different college requirements when I was in school cause of learning and adhd problems. When I went to the professor and explained why a particular thing was really challenging they usually worked with me. When I have to talk about mental health problems I try to detach myself from it. I accept that that is my limitation at the moment and don't judge myself for it. It just is how it is and I explain that to them as accurately as possible. If you pretend to be confident no one really knows you aren't. Someone once told me that was the key to being confident. Pretend to be. Practice what you will say and maybe write down some bullet points to refer to during the skype meeting. I would just say "to be honest the reason why I am not coming in is because I have agoraphobia, generalized anxiety, PTSD and panic attacks. I choose this major because it said it was fully online and at this time I am not able to come to regular classroom settings however, I still wanted to get a college degree. This assignment is really stressing me out. I wasn't expecting something like this. This is outside of my abilities right now. This is why I choose to take an online major." Or something to that effect. Be straight forward. Don't forget to practice it and write down bullet points. I do that every time I have a meeting or something or a phone call. Even when it's the simplest thing. It really helps when I panic and my mind goes blank. Sometimes I will write out a whole first sentence or two and so if it goes blank I can read those and that gets me going and then I have bullet points to keep me focused and from forgetting things. Tell him that you can get a letter from your therapist confirming this and ask if there is any accommodations he can make or an alternate assignment. Talk with him and go in expecting it to go well. A lot of times they aren't that strict and if you explain all of that he might be like yeah we can work something out. Also have you looked into the disability services? I was registered with them in college for ADHD but they also gave services to people with mental health issues like anxiety and depression. Your college should have an office. I would call them asap and ask to speak to someone. I would explain your diagnoses and ask what support they can offer you and how you can register asap. Be completely honest about the situation and your limitations. Tell them what you can and can't do. If you have documents to prove this and a letter from a therapist and are completely honest i think they will work with you and believe you. They won't want to torture you. They also won't want you to fail to earn a degree because these mental health problems effect one assignment. I found the disability services office at every school i looked into to be very helpful, friendly and support of students. They are on your side. You have a very good reason to not want to do this assignment the way it is assigned and have a disability that is recognized by law so legally they need to work with you. Maybe you can do the speech on skype and he can record it and show it to a class for them to evaluate or something. But I would address this asap. Be up front with him and contact disability services and don't be ashamed. This is not your fault. This is what you are dealing with and you are doing the best you can. If he isn't willing to work with you, disability services should be able to advocate for you. But be prepared to present documents proving that you have these issues. A letter from your therapist might help too. But for all we know, when you tell the prof he might be like "I completely understand. We can work an alternative assignment out for you". If you need any more support feel free to message me. I have a lot of experience working with professors and disability service offices for the support I knew I was entitled to.