What do you mean by holding a birdcage with a gun?

This phrase can be used to describe a person who has both a tough personality and a gentle personality.

Holding a gun and carrying a birdcage is used to describe a person who is both hard and soft, or to describe a person who is tough and soft in handling things.

The specific meaning may vary according to the context. This sentence can also be used to describe a person's ability to cope with complex situations, which can be as decisive and resolute as "holding a gun" and as careful and patient as "holding a birdcage".