When we honor Mary, we also show her honor as our spiritual mother. First, we know that Jesus honored her.
In John 2: 1-12, we see on occasion of the Wedding at Cana that Jesus appears to rebuke her. Likewise, he seems to downplay the role of his mother on two other occasions when she is referenced, in Luke 8: 19-21 and again in Luke 11: 27-28.
However, this is a mis-interpretation of these events. Jesus would never rebuke or downplay the importance of his mother. Jesus was the perfection of a good Jew. Jesus would have perfectly obeyed the commandment to Honor your Father and Mother, and he would have obeyed it perfectly. In turn, we are called to imitate Jesus and we would also honor Mary, as Jesus' mother, and as our Mother too.
How do Catholics come to the conclusion that Mary is our mother? First Catholics believe that when Jesus entrusted Mary to John at the foot of the cross he was spiritually making Mary our mother as well. While we believe this, we acknowledge that there is no proof text here. This passage does not provide Biblical proof to support regarding Mary as our mother but the connection is of great spiritual imporantce to us.
Therefore, we must also remember to pair it with Revelation 12:17. This verse does directly establish the motherhood of Mary to us. It calls the Woman the mother of all who follow her son.
Rev 12:17 Then the dragon became angry with the woman and went off to wage war against the rest of her offspring, those who keep God's commandments and bear witness to Jesus.
As you can see, contrary to being a "man-made tradition;" this belief is strongly rooted in scripture.