I am 56 years old, would benefit from meditation, but the feelings of panic and claustrophobia have always put an end to my many attempts over my lifetime. I would rather exit the room than have someone talk me through a breathing exercise. It's as if I feel threatened. Why is this?
Present moment awareness during your everyday activities may be a better path for you.
For example, when you are brushing your teeth, stay with that in the moment, without racing ahead to all things you need to do or becoming alarmed over the things you haven’t done. Really get into the feeling of being here and now. When you are in the now, the fear that is the basis of anger dissolves. You are all right now. Nothing is threatening you. You can be at peace.
Being 56 years old, you have many past experiences that can obtrude upon your peace of mind and trigger anger. While you are meditating in the style you mention, you may be opening the floodgates of your consciousness to all the fearful and upsetting moments when you felt you were not in control. Therefore, letting go and just allowing yourself to be, while you sit and watch your breathing is not effective for you.
Also, too much effort, such as trying very hard to concentrate on your breathing can put you in a situation in which, while you are waiting for something miraculous to happen, you are feeling nothing of the sort and so anger and frustration arise.
I do not believe meditation should be stressful, effortful, a chore, something to be done to ensure salvation, or anything other than a pleasure in itself. It is not a means to an end, or just one more thing you have to go through to get where you want. It is just one way to get in touch with the ground of your being.
It sounds like you need some more direct instruction in Transcendental Meditation than just being led in a guided meditation exercise. If you decide to continue your pursuit of meditation, enroll in a TM course. You will learn how to deal with the anger and upset that comes up for you, among many other life-changing techniques.