Being wrong in public stings for a day. Staying wrong in private costs you for years.

Being corrected in front of people is uncomfortable for a short, sharp period and then it is over. Holding on to a wrong idea quietly is comfortable indefinitely and expensive the whole time, because everything you build on top of it inherits the error. The costs are wildly asymmetric.

When you suspect you have got something wrong, say so early and plainly rather than defending it. The embarrassment is an afternoon. The alternative is a decision made on bad information every time the subject comes up.