I used to interpret this song as a yearning for freedom/independence. I don’t know what the artist intended but I feel like it is a reference back to a line in “Mother” by Pink Floyd on The Wall “Mama’s gonna keep you right here under her wing. She won’t let you fly but she might let you sing”
I don't think it's as complicated as all that. I think Gilmour just likes to fly. Per Wikipedia:
Gilmour is an experienced pilot and aviation enthusiast. Under the aegis of his company, Intrepid Aviation,[26] he had amassed a collection of historical aircraft. He later decided to sell the company, which he had started as a hobby, feeling that it was becoming too commercial for him to handle. In a BBC interview, he stated:
Intrepid Aviation was a way for me to make my hobby pay for itself a little bit, but gradually over a few years Intrepid Aviation became a business because you have to be businesslike about it. Suddenly I found instead of it being a hobby and me enjoying myself, it was a business and so I sold it. I don't have Intrepid Aviation any more. I just have a nice old biplane that I pop up, wander around the skies in sometimes...
It was about taking flying lessons and becoming a licensed pilot back in the day.