Some years back, whilst defending the frontier as an Immigration Officer at Heathrow, there were passengers from a flight from Sydney coming through. One came to my desk...I looked at him and said "Why are you wearing a parachute?" He told me had had been wearing it the whole trip and I was the first to notice! As he said, imagine how it would feel if everything went pearshaped and your parachute was down with the baggage.....
As for personal flying phobia, I also get the "trapped under the wires" dream...high speed, very low but the aeroplane responds so slowly I can't find my way up through a gap. There's a sequence in a film called "Porco Rosso" ( a weird cartoon) which is very close to the feeling.