We can assume that W.B. Yeats' experiences have served to influence the things he wishes for his daughter in the poem, "A Prayer for My Daughter."
The first thing Yeats wishes is that his daughter will be given beauty, but not the kind that will distract others or herself—that others might become "distraught" by her beauty, or that she might become too preoccupied with her own image in the mirror. For some people, beauty becomes more important than anything and the pursuit of beauty leads one to believe that having it means that nothing else is important in life. For some, having beauty robs them of "natural kindness," as well as honest "intimacy," which allow one to make the right choices—rather than to idolize beauty to the extent of all else, and not ever be able to find a true friend.
Yeats alludes to famous women who were considered beautiful, and that life wasn't actually so great for them. He speaks of Helen of Troy and Venus, the goddess of love. Yeats knows that beauty is fleeting: what he wishes for his daughter is to have knowledge or "have her chiefly learned..." of "courtesy."
Yeats has experience the pain that accompanies great beauty in a woman, in his love for Maud Gonne (an "actress and political activist"). While beautiful, this woman (who he met at twenty-two and wooed for almost thirty years) did not have the special qualities of the woman who Yeats ultimately married, Georgie Hyde-Lees. Gonne's beauty brought her no satisfaction, and left Yeats greatly frustrated:
Yeats suggests that kindness and generosity breed trust and affection between people. Yeats would also wish his daughter a life of stability and deep-rootedness—that is, a quiet life away from noisy thoroughfares.
Yeats did not want his daughter deeply involved with the very things that seemed in his mind to be distressful:
..."intellectual, political, financial, or emotional struggle."
He wanted his daughter to think less about her appearance and "cultivate her own personal worth...and her soul." Yeats' experiences with Gonne and then his wife showed two very different women, and based upon his relationships with both women, he seemed to believe that the characteristics his wife had were the qualities most admirable, and those he hoped his daughter would also have also.