Smiles are contagious and when you smile at someone they can’t help but smile back and if you scowl at someone they are likely to scowl back.
But in this quote instead of externally showing kindness, Wayne Dyer is saying that if you give yourself kindness then it becomes easier to show kindness to others.
If you are looking to improve how you react to others try reacting better to yourself. Do you know the phrase you cannot love another until you love yourself? It has some similarities.