In A Doll's House, why does Mrs. Linde think that Dr. Rank was the person Nora borrowed money from?

Christine Linde’s belief that Dr. Rank is the man that loaned the money to Nora, which is false, as it was Krogstad who did it, can be found in Act 2 of the play.

Christine goes to visit Nora, who had asked for her to come so that Christine can fix the Neapolitan girl dress that Nora wanted to wear to the ball. As they speak, Christine asks about Dr. Rank, and asks Nora what is wrong with him. Here, Nora explains to Christine the condition of which Dr. Rank is dying, which surprises Christine, as she had no idea that Nora had any awareness of anything or anyone else besides her (Nora's) own issues. This is indicative that even Christine, as much as she knows and loves Nora, also sees her as someone who is not much more capable to be anything but ornamental.

After asking more information about the doctor, Linde puts the facts together and infers that this has to be the mysterious man. Dr. Rank is rich, he goes to the house a lot, is friends with Torvald, and is trusted by the Helmers. Christine furthermore felt that Rank was a “tactless” man by getting into monetary dealings with Nora behind Torvald’s back.

Mrs Linde. Don't prevaricate, Nora. Do you suppose I don't guess who lent you the two hundred and fifty pounds?

Nora. Are you out of your senses? How can you think of such a thing! A friend of ours, who comes here every day! Do you realise what a horribly painful position that would be?

Mrs Linde. Then it really isn't he?

Nora. No, certainly not. It would never have entered into my head for a moment. Besides, he had no money to lend then; he came into his money afterwards.

Essentially, the reason why Christine thinks that Rank is responsible is merely by assumption, after making an association of facts. He would have been the prime candidate. He is a bachelor who pays a lot of attention to Nora, has the money to give to her if she needed it, and he is in good graces with Torvald. It is no surprise that Christine would have suspected him to be the mystery man of whom Nora spoke. However, Christine was wrong. Her old flame, Krogstad, was the person who lent Nora the money and is now blackmailing her for it.