I heard it said like this – we need to have baby skin and elephant skin at the same time. Baby skin to help those that are hurting, those that are new Christians and those who are searching for Jesus. In other words, we are to have baby skin to feel and empathize with those that are vulnerable. This will allow God to work in their lives so that He can be their strength.
At the same time, we also need to have elephant skin for those that hurt us un-intentionally, those that hurt us intentionally and those that want their way, regardless of the cost and sometimes at our expense. In other words, we need to be strong in the Lord so that we do not get upset or side tracked easily.
Having only one type can make us become bitter as there is no balance.
However, having both types of skin help us to get better and not bitter.
I am sending you out like sheep among wolves. Therefore, be as shrewd as snakes and as innocent as doves. – Matthew 10:16 (NIV)