Treating someone the way you would want to be treated means responding based on how you would like someone to respond to you. For example, if I am upset, I may want someone to give me advice, so I might do the same for someone else.
On the other hand, responding in a way that meets their needs means thinking about what the other person needs at that moment. They may want advice, or they may just need someone to listen and understand them, or even give them some space. It is about putting their needs first instead of assuming they want the same thing I would want.
