No matter how well you ease into a tough topic the person may still react strongly. Avoid using that reaction to blame the other party or to not raise the issue at all. No ideal time often exists for difficult topics, but there are better times. Consider setting a future time, to allow the other person to prepare for such a discussion. Send a signal that the topic is manageable to reduce anxiety. Going into your own mistakes is rarely easy but uniquely powerful. Share the deeper reasons for raising the topic to frame the conversation positively.
"People only see what they are prepared to see." Ralph Waldo Emerson