Flying machines seem unsafe because the pilot has limited control. Birds can quickly change the shape of their wing more drastically than planes or hang gliders, so there are less unrecoverable situations.
> “You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes.”
J B S Haldane
https://www.phys.ufl.edu/courses/phy3221/spring10/HaldaneRig...
Also, of course, many birds do die.