to refuse to change what you believe is right or what you want to happen.
Be firm on important issues, but do not dig in your heels at every opportunity.
dig in (one's) heels
To cling stubbornly to one's beliefs or wishes. Please let me tell my side of the story before you dig in your heels on this, OK?Well, I told Grace she can't go, and now she's dug in her heels as if this party is the most important thing in her life.
dig in (one's) heels
To resist opposition stubbornly; refuse to yield or compromise.