Why does Kristine encourage Krogstad to let Torvald read the letter revealing Nora's deception in A Doll's House?
Act III of A Doll's House shows Mrs. Linde and Krogstad opening up about many realities taking place in the play. One of them is their own realities; they are both older than when they first met. They are also alone, and in need of someone to take care of their emotional needs.
The second issue is the mirror relationship between Nora and Helmer. It is a reflective relationship to that of Linde and Krogstad in that new dynamics are taking place, only inversely. Linde and Krogstad are two lonely souls finding out about each other's sadness and, as a result, getting together at last.
Conversely, Nora and Torvald are a seemingly-strong marriage which is about to endure having to learn the truth about one another and, as a result, they will be dissolved forever.
Mrs. Linde is aware of this; she knows about the lies and pretenses that Nora lives under. She believes in Nora as a better and stronger woman than to live her life as Torvald's play thing.
Hence, the main reason is that Mrs. Linde wants Nora to experience a life without lies and unneccesary pretension. She wants her and Helmer to open up to each other and be a real couple. The fake issues must end. In all, it is all for Nora's own benefit.
This is why, when Krogstand decides to recall his letter, her answer is:
MRS. LINDE:...twenty-four hours have elapsed since then, and in that time I have witnessed incredible things in this house. Helmer must know all about it. This unhappy secret must be disclosed; they must have a complete understanding between them, which is impossible with all this concealment and falsehood going on.