'Stick your neck out for someone or something' is an informal expression meaning 'to do or say something when there is a risk that you may be wrong': 'Why should I stick my neck out to do something for her? What has she ever done for me?' 'He made a risky investment. He stuck his neck out for the deal because he thought he could make some money.'

to "stick your neck out" means to take a risk by helping someone