Is Accepting others mistake wrong in acaemia?
If they are wrong, Instead of being harsh, I try to accept their argument then explain my argument. 


I think the problem may be this false dichotomy. 

Imagine a student comes to you and says "I think the Earth is flat because I went to the top of a tower in the midwest and everything looks flat."


One option (what it sounds like you're doing) is saying okay, that makes sense, but there is evidence the Earth is round -- satellites, circum-navigation experiences, etc. 
Another option (what it sounds like you're complaining about) is saying no, that's not a good argument, the Earth is large enough that apparent flatness on the scale of ~50 miles does not imply that the entire 26,000 mile Earth is flat.


Of these, the second has a clear advantage, in that it actually addresses the actual reason the student is confused. Just telling the student how to do it properly is no more helpful than telling him to read the textbook; explaining where the student's thinking is incorrect is where you can be really helpful. 

Of course, same goes for colleagues rather than students -- when dealing with a disagreement, you need to both defend your ideas and refute their ideas. Otherwise you're both just restating your positions and not actually resolving anything. 

Now the reason I called this a false dichotomy is because there is no need to be harsh when refuting others' ideas. The best way is to ask leading questions so that the they realizes their mistake all on their own. Usually, doing this requires an excellent understanding of the subject matter. When dealing with colleagues on research topics, one may not have a strong enough understanding to do this gracefully, resulting in what seems like harshness (or one may just be a jerk).