Letting someone believe something false because correcting it is awkward is still deceiving them.

Silence can carry a false impression perfectly well. If somebody has the wrong picture and you know it, every minute you leave it standing is a choice, even though you never said anything untrue. What stops the correction is usually the small social cost of interrupting, which gets paid later anyway with interest.

When you notice somebody working from a wrong assumption about you, fix it in the next sentence rather than at the end of the conversation. A short, flat correction barely registers. Waiting until they have built something on it is what turns a remark into a confession.