My insecurity comes when there is a serious incongruency between what is being said and the person's actions.
Or between what is being said to one and what is being said to another.
Say what you mean, mean what you say, and if the answer is "I am having an issue, I need time to process and I will talk to you if I need to later" then SAY that - don't tell me you're fine, that nothing is wrong.
Don't tell me one thing and then tell someone else something different - it leads to mistrust.
There are three sides to every story - yours, mine and the truth.