Let me provide some background. Some friends of mine brought an Anglican friend (who has a genuine interest in Catholicism) with them to Mass. He and I had earlier talked about the fact that his "Anglo-Catholic" parish takes a very high view of the Eucharist, believing in the Real Presence in some sense. Through God's mysterious Providence, the homily was on the difference between the Anglican and Catholic understanding of the Eucharist (I love when God does things like this). Father talked about an Anglican seminarian who didn't understand why he couldn't receive at Mass, and the priest he'd been speaking to responded, "Do you worship the consecrated Eucharist with the worship due to God alone?" The Anglican conceded that he didn't, and the gulf between the two views was made clear.
Since yesterday was the Feast of Corpus Christi, we had a Eucharistic procession after Mass, going from the church to the church cemetery. Upon arriving, we worshiped Christ in the Eucharist and prayed the rosary. Afterwards, I had a chance to sit down with my Anglican friend, and we talked a bit about what had happened. He'd been struck by Father's homily, which convinced him to join us in adoration. But he had been disconcerted by the fact that we were praying the rosary: if what Father had said was true, that this was God Himself, why take time away from worshiping Him to honor Mary?
After thinking about it for a bit, I came up with two explanations. I'm curious what others think of these, and how they might have answered the question themselves:
1) One of the highest honors you can pay someone is to respect and honor their loved ones.
For example, one of the best compliments you can give a man is to compliment his mother, wife, or children, those people he feels protective of. Complement him personally, absolutely, but tell him he has a good family, and you've really paid him a compliment.
Likewise with Christ. Mary isn't trying to become the fourth member of the Trinity, or steal Jesus' spot. And God isn't insecure or jealous of Her. Instead, He lavishes Her with honors, so that She's "clothed with the sun, with the moon under Her feet and a crown of twelve stars on Her head" (Rev 12:1), and She says of Herself in Luke 1:48-49, "From now on all generations will call Me Blessed, for the Mighty One has done great things for Me." And Christ makes clear that He loves and honors His Mother. In addition to being Her God, He's also Her Son. And like any loving Son, He thrills at seeing His Mother honored.
2) We should be very wary of pitting good against good.
On the surface, my friend's question is a very good one. Every moment we pray to Mary is a moment we're not praying to the God in front of us, right? But I was reminded of Mark 14:3-5:
While he was in Bethany, reclining at the table in the home of a man known as Simon the Leper, a woman came with an alabaster jar of very expensive perfume, made of pure nard. She broke the jar and poured the perfume on his head.Some of those present were saying indignantly to one another, “Why this waste of perfume? It could have been sold for more than a year’s wages and the money given to the poor.” And they rebuked her harshly.In fact, it's apparently in response to this that Judas decides to betray Christ (Mark 14:10). So the woman has done a good thing, and the response of Judas and the others is essentially that it's not the best thing she could have done with that money (Christ actually disputes this, by the way - Mark 14:9). My point is that there's always a demonic desire to turn good against good. Every moment spent helping the poor could be spent in prayer, every dollar spent on building beautiful churches could be spent on the poor, every minute praying to Mary could be spent praying to Jesus.
We become incredibly stingy with our time, talent, and treasure when it comes to doing those things which are pleasing to God. But do we ever hear people say, "every dollar spent on amusements could be spent helping the poor," or "every moment watching TV could be spent praying to Jesus"? If so, it's much less common. For that matter, every moment spent criticizing another Christian for helping the poor, or donating to the Church, or praying to Mary could be spent doing something good for God, like praying, rather than tearing apart the Body of Christ. So instead of making one good the enemy of the other, why not spend all the time you want praying to Mary, and all the time you want praying to Jesus, to the Father, and to the Holy Spirit? If you find you have less time for TV or back-biting against other Christians, those are sacrifices that are much more worthy of being made.
Finally, Scripture tells us, "confess your sins to each other and pray for each other so that you may be healed. The prayer of a righteous man is powerful and effective" (James 5:16). So every moment in prayer to Mary, telling Her our troubles, asking Her for Her prayers, is a moment in obedience to God and Sacred Scripture.