Psalms 27:12

Deliver me not over to the will of my adversaries,

For false witnesses are risen up against me,

And such as breathe out cruelty.

So with his confidence somewhat restored he asks that his life might not be subjected to what his opponents want for him, for they have risen up against him and maligned him, and have spoken about him cruelly, which is no doubt why his family have rejected him. The last thing therefore that he wants is to be subject to their will.