People don't like to admit they're wrong. It's a natural human defence mechanism.
It is a mistake to think someone has to admit they are wrong. The majority of times, there is no reason to push for it. You need to step back yourself, and ask if this argument is going to matter in two weeks, two months, or two years. If the answer is no, likely, your best bet is to just drop it.
Yes, the male spouse will often refuse to admit he has been cheating on his wife because they feel guilty and even while having the affair they feel it is wrong so they will lie no matter how much evidence is against them.
They do not want to admit they are wrong and may not think they are in the wrong as well as we have been led to believe by society to place blame rather than take responsibility for it.
They weren't wrong...
A sentence using the word admit could be this, "The man on trial did not want to admit he was wrong."
Pride. Usually involving an ego to hide an insecurity within themselves.
women never admit that they wrong cause they always right
"Wrong war, with the wrong people, at the wrong place, at the wrong time!" And "...Trying to isolate this war, NOT MAKE A BIGGER ONE!"
Because people want the best of both worlds
Always. Narcissists never admit to being wrong - even when they are.
confess
You cannot make someone admit they are wrong. You know you are right; they are wrong and that is all you need to know. If this person has done something terrible then try to get them to be responsible for their own actions and if they do not then break away from this person. If it's a crime then report it to the police. If it's gossip that has hurt someone then the person who will not admit to doing the wrong will pay for their mistakes eventually.