When I decided to stop annoying my friends with bike-related nonsense and start a blog I chose "Liberation Cycling" because it captures a number of things about me. I realized that I never really fulfilled a semi-promise from my first post, which was to explain the name, and since I've been thinking about it recently, why not?
This week I've had to drive to work. Yesterday specifically drove home the freedom that you lose driving (when you should/could be riding). I got stuck on a road where a delivery truck for a construction site had blocked off one of the two lanes of a major commute-direction street. This led to a significant back-up stretching through two lights. As I sat there all I could think about was that I could be dodging the whole thing on my bike. The freedom of cycling.
Another aspect of it for me is the clarity of mind that develops, primarily on longer rides, when you can settle into a cadence and ride. No shifting, little effort, just riding. I miss that here, since there aren't easy places to take longer rides that aren't crowded MUPs, and can't wait to get back to CA and have the backroads I know available practically at my door.
The last aspect of liberation that I get from a bike, or at least the last significant one, is the freedom of movement. Not just freedom in commuting, discussed above, but true freedom of movement. Bikes allow you to go anywhere, and with a little preparation (or a high-limit credit card) you can go everywhere. Getting around town is easier on a bike, taking a vacation (touring) isn't necessarily easier, but it is certainly more open to changes of whim. There are very few barriers that can stop a person with a bike.
Those are a few of the ways I see bikes as liberating. There may be others for you, and there are some other, smaller ones for me.