Telling ninety percent of the truth and hiding the important ten is still lying.

A mostly true account can mislead further than a flat refusal to answer, because it buys belief for the part you left out. The missing piece is usually the one that would change what the other person decides, which is exactly why it went missing. Accuracy in the details does not make the whole thing honest.

Before the next difficult conversation, work out which piece you are hoping not to mention. That is the part to lead with. Saying it yourself is a far smaller event than having it come out later.