Brian Cutler advises actors to eliminate the habit of apologizing on set, as it can create doubt among the crew and signal insecurity. Apologizing too frequently can fluster the actor and those around them, potentially undermining the confidence others have in their capability to perform. Cutler suggests practicing self-assurance in everyday situations to build this mindset, reminding actors that they were chosen for the role for a reason and should uphold their self-worth without unnecessary apologies.