"One of the teachers in the music academy told me there was no solo percussionist - the profession simply didn't exist," says the renowned, multi-award-winning 47-year-old Scottish musician, who performed with the City Chamber Orchestra of Hong Kong at City Hall last night. "When I was told I couldn't do it, it just made me want to do it more."
Glennie, made a Dame in 2007 by Britain's Queen Elizabeth for her services to music and education, plays dozens of different percussion instruments, including drums, marimba and vibraphone.
She has recorded with musicians, including DJ Yoda, "Beat Boxer" Shlomo, the Japanese drumming trio Kodo, and Sting; two of her 28 solo albums won Grammy Awards, while she has commissioned world-renowned composers to write 170 works for solo percussion.
Millions of people around the world watched as she led a performance by 1,000 drummers at the opening ceremony of the 2012 London Olympics.
Her success is all the more remarkable because she has been profoundly deaf since the age of 12, following a severe ear infection. Today, she relies on hearing aids and often performs and records barefoot because it helps her to feel vibrations through the floor and her own body.
"I didn't really know I was going to be deaf; I just adapted to the condition and lived with it," she says.
Not that she considered herself handicapped; she pursued her dream to be a musician, and left home at 16 for London, where she studied percussion at the Royal Academy of Music.
Growing up on a farm, caring for sick lambs, made her believe in herself, she says. "With responsibility comes trust and assurance that I can handle things. I won't let anybody or anything stop me from doing what I want to do."
Her goal was always to be a solo percussionist. But she knew she had to create her own opportunities. "I wrote to ask composers if they could write some work for me," she says. "I visited orchestras and asked if they had any percussion concerto coming up. They all looked at me like I was from Mars."
Eventually one conductor contacted her; the rest is history.
Her deafness might seem unfortunate to other people, but she says it gives her a unique experience and understanding of sounds and what "listening" means. "Listening is being aware. It means focus and concentrating on the person you are with, or the thing you're doing - right now."
People today are too busy texting on their phones and communicating on social network platforms, she says; they miss out on what is in front of them.
"When I'm talking to you, you're the most important person, right now," she says. "I can't really talk to you when I'm looking at other people. That connection is what we're missing.
"Listening is 'wanting to be there'. Like a performer in an orchestra, you want to be on stage. Listening also takes time; life is a journey of self-discovery and it takes time to explore. As youngsters, you need to take time to discover yourself and explore possibilities ... listen to yourself, and answer your own questions.
"People will say things that deflate you. Just get used to it and believe in what you do. Keep your goal simple and create opportunities for yourself to get there. You'll find a lot of opportunities at your doorstep."