Of course this happens to us all the time. It happens in the face of others' opinions about the matter we are discussing, when the others have an opinion different to our own. Only when we feel secure within ourselves, are we strong enough to hold to our own truth.
This is a topic that makes some people squirm with unease. It's not fun to look at this aspect of yourself, but what is really important about it, is the fact the opinions of others don't tell you anything about your own truth. In order to stick to your own truth, understand that by changing your belief or backing down when others tell you why your opinion couldn't possibly be right, you are tacitly saying that their opinion has greater value than yours. In effect what you are also telling yourself is that your own way of seeing a particular matter, is not as worthwhile as that of the other person, or that the other person has a greater right to an opinion than you.
And that is evidently not true.
The opinions of others are not your truth.