They somehow feel that honoring the Virgin Mary is taking away from Jesus -- as if that was possible! Take a look at the "Jesus is our Mediator, not Mary" answers, and you'll see what I mean.
I think the problem is that they don't understand the difference between a mediator and an intercessor. There *is* only one Mediator in the matter of sin, and that's Jesus. He paid the price for our sins, and He Alone can stand before God and reconcile us to the Father -- which is what a mediator does. Only Jesus can say, "Father, I died for this person, who has accepted my blood offering for his sins. There is no more enmity between You and him."
An intercessor, however, is one who speaks to someone on behalf of another person. We have many intercessors with God: family, friends, our pastor, people at church, etc. They pray for us and ask God to help us, just as a friend of a company president might put in a good word on your behalf if you're wanting a job.
Mary is an intercessor for all those who ask her prayers -- not a would-be rival to Jesus in His role of Mediator. Perhaps if Protestants understood that crucial difference, they wouldn't feel so threatened by our Blessed Mother.
She has nothing but love and prayer for the people Her Son purchased with His Precious Blood, just as any other mother would care for her children.
And if Protestants understood the difference between latria (worship, which is due to God and Him Alone), dulia (honor, which is given to the saints), and hyperdulia (great honor, given to the Blessed Mother), they would know that we DO NOT worship Mary.
Only God is worthy of our worship because it would be idolatry to worship anyone or anything except Him. That's what the Bible and the Church teach, and that's what we Catholics believe.
Loving the Blessed Mother and asking for her prayers in no way constitutes worship. Sorry to burst some Protestant bubbles, but those are the facts.