Most parents don't apologise to children when they've been wrong (snapped unfairly, broken a promise, made an error). The avoidance protects parental authority but models that adults don't apologise — a pattern children carry into their own adulthood.
What this looks like
'I lost my temper earlier when I shouldn't have. I'm sorry. That wasn't your fault.' Brief, specific, no over-explaining. Doesn't undermine authority; demonstrates emotional skill.
Why this matters
Models adult accountability. Teaches that apology is not weakness. Strengthens parent-child relationship. Children of apologising parents apologise as adults; children of never-apologising parents often struggle to.
Apologise when warranted. The relationship and the child's emotional development benefit. Most parents fear it undermines authority; usually it strengthens it.