The phrase "to give an inch" means to compromise or yield a small amount in a situation where you are being stubborn or unwilling to budge. Full definition
I wasn't prepared to give an inch on much at all by that stage. (housegoeshome.com)
Unlike many other titles that simply look to make you feel awesome for accomplishing something everyone else can, this one sets out a challenge and never gives an inch. (playstationlifestyle.net)
Do not give an inch in teaching children that this could possibly be a good thing. (nakedpastor.com)