Bird or the cage?

Elizabeth: Mr. DeWitt–here!
A Gentleman: Bird?
A Lady: Or the cage?
A Gentleman: Or perhaps the bird?
A Lady: Nothing beats the cage.
Booker: These two again? How do– …Never mind.
Elizabeth: Look at these, they’re amazing! Which one do you like more? This one…or this? The bird is beautiful, and… the cage is somber, but there’s really something special about it. I just can’t decide.
- Bioshock Infinite

Does it even need to be said?

Our little Icarus would rather rip his own wings off, if it prevented them from getting clipped again or if he thought the cage door was closing.

He will not be caged. Even the illusion to putting him in a cage, literal or metaphorical, will make sure that Tyson never returns.

Tyson would rather fly free, and have the trust from someone else that he will always come back. That so long as the door remains open, Tyson will tumble in through the window instead.

He assumes that it’s part of being a soldier: the romance of being on the road, always having someone waiting back home, et cetera. That’s more of a commitment to him, than being tied down: having to trust that whilst the other is away, they’re happy and that they’ll be coming back home eventually.

Tyson isn’t someone who will move in with you, but he will climb through your fourth-floor apartment window with a cavalier - devil may care - smile and stay for as long as he can, then leave the way he came with a promise to come back soon.

Which is why his arrangement with the Moriarty Mirrors works.

Employment to the web is for life. You cannot leave.

And yet, The Moriarty Mirrors can tell Tyson with complete sincerity that ‘he is free to leave at any time’, because he never will. And they all know it. There is no danger in allowing Tyson to remove his leash. He will always come back. He will not betray them.

Tyson knows that it’s a far bigger trap than an actual cage. That his loyalty will be his undoing. Yet so long as he has the choice to leave, Tyson will always remain as their loyal Pup instead.