I think that the instantaneous hang-up, which is not so much intellectual as it is merely reactive, is the notion of praying through her. As you mentioned, I was raised with a protestant background, and you only pray to Christ. I mean, there is a kind of nondescript reference to The Father, where people often pray the word 'God', but without clear designation of the Father. It always felt as if (and as if it became imprinted on me this way) you prayed to the Father when you said God, and to Jesus at any other point. There wasn't really any theological discussion on the trinity at any point. What I was exposed to in the Church of God was a lot of psychology, really - a lot to do with the struggles of life, whether these were emotional, financial, marital, etc., with a reference to some scripture to back up the 'therapy session'. Needless to say, it felt barren for myself and a few others. Of course, you know that some people just aren't inclined to the intellectual aspects of things anyway, so such a complaint would never occur to them. If the so-called sermon was enough to get their 'feels' engaged, they were good for the week.
Revelation 8:3-4 (biblegateway.com) refers to angels receiving prayers from the saints and then offering them to God. Tradition understands that the saints and angels of heaven play this mediating role, insofar as they purify our prayers before they reach God - which is obviously an explanation that has to be understood in context. It's not as if God is blind to our prayers before they are "purified", but rather, it is just another case of God willing to accomplish His will through creatures, through the Elohim (of which He is not Himself entirely separate, but in which He is immanent, as the im (inverted mi) part indicates).
Revelation 5:8-14 (biblegateway.com) shows the same kind of thing, but this time the "elders" are receiving and offering the prayers.
Likewise there is James 5:16 (biblegateway.com), where Scripture commands us to pray for one another, and affirms that the prayers of the righteous "availeth much". Who is more righteous than Mary? Or are we to pretend that only those still alive can pray for us? Recall the Threefold Body of Christ and the Threefold form of the Church - Church Militant, Church Suffering, Church Triumphant: all one Church. In the Apostle's Creed, which we pray in every Mass, we affirm our belief in "the communion of saints". This does not exclude the saints in heaven; if anything, it refers to them most of all, since they alone "can sin no more", since they have the benefit of the full vision of God in the Beatific Vision.
And Jesus Himself communed with the dead at the Transfiguration, speaking to Elijah and Moses (Matthew 17:3 (biblegateway.com)).
And of course the Books of the Bible canonized by the Church, but which Protestants conveniently threw out lend support to this notion of praying for the dead:
43 And making a gathering, he sent twelve thousand drachms of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection,
44 (For if he had not hoped that they that were slain should rise again, it would have seemed superfluous and vain to pray for the dead,)
45 And because he considered that they who had fallen asleep with godliness, had great grace laid up for them.
46 It is therefore a holy and wholesome thought to pray for the dead, that they may be loosed from sins.
(2 Maccabees 12:43-46 (biblegateway.com))
which is the Scriptural basis for Purgatory. But if we of the Church Militant, for whom salvation is not yet guaranteed, can pray for the Church Suffering, for whom salvation is guaranteed, all the more should the Church Suffering, and most of all the Church Triumphant, be able to pray for us. We are all one Church, one communion of faithful, and we are in this together.
So praying to Mary is nothing more than asking a person, a saint no less, that we know to be exceedingly holy, to pray for us to God. That James verse makes clear that God wills that we do more than just ask Him directly for help; He wills that we ask His saints for their prayers also, and Mary is the best choice in this regard. God's love for Mary is so great that it is nothing but pleasing to Him when His faithful approach her to ask for help, and Mary's love for the Lord is so unwavering and complete that she can scarcely help but lead us to her Son.
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