hold out
hold out {v. phr.}
1. To put forward; reach out; extend; offer.
Mr. Ryan held out his hand in welcome.
The clerk held out a dress for Martha to try on.
The Company held out many fine promises to Jack in order to get him to work for them.
2. To keep resisting; not yield; refuse to give up.
The city held out for six months under siege.
3. To refuse to agree or settle until one's wishes have been agreed to.
The strikers held out for a raise of five cents an hour.
4. {slang}
To keep something from; refuse information or belongings to which someone has a right.
Mr. Porters partner held out on him when the big payment came in.
Mother gave Bobby cookies for all the children in the yard, but he held out on them and ate the cookies himself.
John knew that the family would go to the beach Saturday, but he held out on his brother.
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Source: A Dictionary of American Idioms