If an interviewer is clearly antagonistic, what can I do?

First, try to relax. Make sure you fully understand the intent of the construction interviewer's antagonism. Ask them if there might be a problem and if there would be a better time to meet with them. Sometimes, an construction interviewer is just having a bad day. Questions of concern can jar them into getting back on track. Sometimes, it's best just to make a graceful exit. Excuse yourself and suggest that there might be a better time to meet. In the end, you need a fit that includes both you and the construction employer environment.