Why do catholics pray to Mary?Well, first you need to know why it would be permissible to pray to the saints at all, let alone this particular saint. You can read my explanation of that here.
Now, from among the saints, why Mary? Basically, all the reasons to pray to Mary flow from her personal qualities and her relation to Jesus. Mothers and wives request her prayers because, as a perfect wife and mother, Mary knows exactly what to pray for. She knows the struggles of being a wife and a mother and what it takes to be a good one. Christians struggling with purity pray to her because she was pure. Christians struggling with temptation or engaged in spiritual warfare pray to her because she is the woman who has emnity with satan, who crushes his head (Gen 3:15; cf. this article), and who evaded his pursuits (Rev 12:6,14-16).
Basically, anyone can pray to her and for any reason. She cares greatly for the entire Body of Christ, just as she cared for the literal body of Christ. Just as Sarah was the spiritual mother of the Jews (and of all who "do right", cf. 1 Pet 3:6), Mary is the spiritual mother of "those who keep the commandments of God and bear testimony to Jesus" (Rev 12:17). Her prayer for us will always be powerful because her will was always united with her Son's, and because "the prayer of the righteous availeth much" (Jas 5:16). "The eyes of the Lord are upon the righteous, and his ears are open to their prayer" (1 Pet 3:12).
Also, the command to "Honor your father and mother" is for us all. She is our mother, and we should love her as much as Jesus did. She is also one of many tools--and perhaps the best tool--that the Christian can use to grow closer to Christ. She points to Christ; she is always saying "Do whatever he tells you" (Jn 2:5). She herself was intimately involved in the Father's mission for His Son (Gen 3:15; Mt 1:21-23; Lk 2:34-35; Rev 12:5) and she was always pondering in her heart the mysteries of His life (Lk 2:19,51). When we pray to her in the rosary we are simultaneously contemplating these mysteries as well. No one with a true devotion to her will ever say that she stood between the Son and any man.
And thus, for all these reasons (and probably for many more that I have forgotten to mention) it is good and well to pray for her and to love her.