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Hi, I'd like to help you with your problem.
It sounds like your husband is dealing with a self esteem problem. For some reason, he feels he is not good enough or he feels competitive with those around him. Maybe his other family members have done important things and he feels left out and needs to compete.
No matter the cause of his issue, he is dealing with a poor self esteem. The fact that he denies the lie even when you have confronted him says that he has a great need to hold on to this lie to make himself feel better.
You need to determine if you feel this lie is causing any harm. If not, let him continue. If the people he tells this lie to ask you about it, simply stay out of it. Whatever you chose to say in response, keep it neutral. You should never feel the need to back him up and compromise yourself.
If you can, encourage your husband to talk to a counselor about his problem. He most likely will be resistant, given his need to continue to hold on to this untruth, but it's worth the effort. Offer to go with him, if you think that will help.
A few books that may help give you more insight and help with this include When Your Lover Is a Liar: Healing the Wounds of Deception and Betrayal by Susan Forward and Donna Frazier and The Self-Esteem Workbook by Glenn R. Schiraldi.
I hope this helps you,