The ladder paradox consists of a ladder rushing towards a garage with two open doors. In the actual paradox, proper length of the ladder is greater than that of the garage, but in this case lets consider them to be of the same proper length.
In the frame of the garage, the ladder is Lorentz contracted, and hence it is possible to "trap" the ladder inside the garage. By "trap" I mean that both doors of the garage must be closed while the ladder is completely inside the garage.
But in the frame of the ladder, the garage is Lorentz contracted, and hence it is never possible to "trap" the ladder inside the garage.
If I am able to trap the ladder in one frame, I should be able to do it in the other frame too right? Why then is there this paradox?