Giving and receiving feedback is something important both in day to day life and at work.
This allow us to progress and help other to do so.
However, this is always easier said than done. If not given properly it is very easy to trigger to the other person that feeling of flight or fly. Resulting in people being either defensive or completely ignoring the feedback.
Most of the responsibility reside on the person giving feedback more than on the one receiving it. Similarly to teaching, it is to the teacher to be sure that the students learn and understand, not the other way around.
But worry not, there is definitely a way to do so properly.
1- if this is done during a meeting, it is a better for the person to know in advance that this will be about feedback.
As a manager, you should not have to do it in a sneaky way. If it is so, then you may have to think more about why are you doing so, and as an employee, you may want to ask directly the question.
2- it does not cost much to explain that the feedback is to help to progress. As such, the manager should also communicate that way. As mentioned in the beginning, this should be done to elevate other, not to destroy them. If the feedback is only a negative comment without mentioning how things can improve, it isn’t a very good feedback.
3- Feedback should also be based on facts and examples. It is definitely fair for someone to ignore a “feeling” as they can be very personal and biased. On the other hand, employee should not simply ignore facts.
4- It is also better if feedback is given about things that were agreed and expected. For example, saying that something has not been done when never agreed beforehand is not a good feedback. On the other hand, if something agreed has not been done, that is an excellent opener for feedback.
5- Like every meeting, it should be concluded with actionable points. What need to be done, when, how etc. This is again about setting expectations.
If there is still a clear disagreement between manager and employee, it may be need to ask a mediator to give their opinion about the situation. Either bey organising the meeting with the 3 parties, or by writing discussion.
But again if the all discussion is based on facts, objectives, results, there should not be any disagreement.
It is actually part of manager job to set all of that properly from the start and ease their work at the end.