The biggest reason is lack of movement or exercise. So, by cycling, you have made an important step. However, the second biggest reason people lose flexibility are repetitive movements in a limited range of motion. That's cycling, folks. Especially quadriceps and hamstrings.
Flexible muscles are almost always more resistant to injury than tight muscles.
In some people tight muscles contribute to a lack of coordination. Better posture and less chance of low back pain. Tight hamstrings and low back muscles are one of the biggest factors in low back pain. How many long distance cyclists do you know that haven't had low back problems at some point in their cycling career. A key part of that answer is stretching.