Improvisation in Music

I played an instrument for 9 years in school, and we were never once faced with the opportunity for improvisation. For me, this is probably a good thing because I know that, while I was pretty good at playing my instrument, I would probably freeze up if ever asked to improvise. I've been thinking about why this is. At first, I thought that it was because I was never exposed to the concept of improvisation in music. However, I think it has more to do with the environment I played music in: school. Schools are very focused on performing tasks as close to perfectly as possible, and following rules as closely as possible. In some respects, this is a good thing. But, because of this, music class was like any other class: a place where students strive for perfection. So, how could a music student feel comfortable ignoring the rules and just playing? We are so rarely given the opportunity to just abandon all the rules and let our emotions guide us in this society.
Question: Do you think the environment affect one's ability to improvise?