There are at least two answers to this question.
The first reason that Torvald refuses to admit that he offered Mrs. Linde a job because of Nora's advice is that Torvald sees this as inappropriate. This is supposed to be a business decision. Personal favors should not enter into consideration. Of course, this is just the first, superficial reason.
Torvald also admits that he wanted to fire Krogstad and so needed someone to replace him. Torvald's reason for firing Krogstad is essentially personal. Krogstad was too "familiar" with Torvald at the bank. This leads Torvald to invite Krogstad to the house where he will fire him.
After a confrontation with Krogstad, Torvald decides to fire Krogstad and hire Mrs. Linde in his place.
Torvald feels that this familiarity undermined his authority, so he fires Krogstad.
Additionally, Torvald claims that Krogstad cannot be trusted because he has acted dishonorably in the past. This is another excuse to cover up his personal reasons for firing Krogstad and hiring Mrs. Linde.
Nora's advice to Torvald is clearly not the only motivating factor behind Torvald's decision to hire Mrs. Linde. The anger that Torvald demonstrates in this moment of the play is related to his sense of pride and his desire to be seen as being in control.
Krogstad had undermined Torvald's authority. Nora's advice can be seen in a similar light. She is attempting to tell her husband what to do, as he sees it, and this is unacceptable. He will do what he thinks is right, regardless of the input of others.