Because Mary always points the way to Christ and how loving, serving and obeying Him is the call of all Christians. The Church has never taught that Mary is above or even equal to Christ. The word of Mary are few but they have something to teach all Christians. For example.
Let It Be Done According To Thy Will- Have faith in what God wills for you. For He always acts to our good and because He loves us.
Do Whatever He Tells You- obey the Commands of God. For only good can come of doing so.
My Soul Doth Magnify My Lord and My Spirit Rejoices in God My Savior- Put God first in your life and remember with joy that He came to save us from our sins. To serve our Lord is a great gift not a burden.
Her search for Jesus and her relief at finding Him in the Temple also remind us that we can never have true peace until we have found Christ.
She also was at the foot of the Cross. She witnessed the torture and death of her son, whom she had held and nursed. She saw the same hands that she had grasped pierced by nails. She saw the same forehead she had kissed crowned with thorns. She saw the same body she hadcared for beaten and bloodied. She saw the heart that beat against hers when she held him driven through by a lance. Yet she stayed, because she know that she must follow Christ no matter where it lead. No matter the promise of sorrow and pain given because of that following.
So even if you dismiss the concept of asking Mary to pray for us. Please remember that her example of faith, her obedience to God's will and her refusal to abandon Christ no matter the cost to her own heart. Her words and actions shows a faith that is truly a gift of God's grace.