The willingness to do this often builds bridges that could otherwise never be crossed if they were not there. Acknowledgment helps with this bridge building process. Some people might believe that this is giving in' to the other side. That even opening up to seeing the other side's point of view weakens their position. This is far from the truth and very understandable.
Most people argue positions rather than interests.
Opening yourself up to hearing the other side may very well weaken your position. It also gives greater opportunity to have both sides' interests served. This makes for a much better resolution. Understand that acknowledgment is not agreement. Acknowledgment is merely letting the other side know you are aware of how they are perceiving the situation and possibly connoting understanding.