i think atticus said this because he wanted his children to not judge people in their lives and to have open hearts because one can not ever truly know how the other is feeling. By saying to climb around in their skin he means that to walk in someones shoes is easy but to crawl in their skin and see every inch of their inner being is a whole new thing. shoes can slip on and off your feet with a simple action but being in someone skin is living like them and being exactly them hearing thoughts no one else ever will.