It’s hard to let people go on with incorrect assumptions or conclusions. But you have to learn to do it often.
The more experience and knowledge you gain, the more you must learn to live with not conveying it all. So many situations involve others discussing matters about which you know a lot, but it would not be appropriate to take over the conversation to enlighten them. You have to not only accept their inaccurate discussion, but also suffer them assuming you don’t know anything about it.
This is maturity. And it’s really annoying.