Catholic veneration of Mary is one of the major stumbling blocks for non-Catholics, especially Protestants. Catholics do not worship Mary and cringe at the suggestion. Devotion for Catholics exists on three planes:

Latria: Worship due to God alone. Hyperdulia: Veneration of Mary.
Dulia: Veneration of all other saints.

Only the triune God is due actual worship; however, Mary points the way to her Son, Jesus. None better.

From the man credited with launching the Protestant Reformation. In his own words:

"No woman is like you. You are more than Eve or Sarah, blessed above all nobility, wisdom, and sanctity." (Sermon, Feast of the Visitation. 1537).

"One should honor Mary as she herself wished and as she expressed it in the Magnificat. She praised God for his deeds. How then can we praise her? The true honor of Mary is the honor of God, the praise of God's grace.. .Mary is nothing for the sake of herself, but for the sake of Christ...Mary does not wish that we come to her, but through her to God." (Explanation of the Magnificat, 1521).

--Martin Luther

Credit: Dave Armstrong, Catholic Culture, 8-24-03, https://www.catholicculture.org/culture/library/view.cfm?id=788

Catholics show too much honor to Mary
by Steve O'Keefe, Staff Apologist

In Romans 13:17, Paul says we should “pay [...] respect to whom respect is due, honor to whom honor is due.” So we need to begin by asking: “What is the appropriate amount of honor owed to Mary?” Let’s take an account.
In Luke 1:46-55, Mary prophecies about the mercy and justice of God, as well as the honor she will receive in the future. And if we look at Matthew 10:41, Jesus encourages us to honor prophets.

In Luke 2:35, Simeon describes the suffering Mary will experience as part of God’s plan of salvation. He says, “A sword will pierce your own soul too.” Correspondingly, in Paul’s letter to the Philippians, he instructs his readers to give great honor to people who have suffered for God’s sake [Phil 2:29].
In John’s Passion account, he recalls Jesus saying to him, regarding Mary, “Behold, your mother” [Jn 19:26]. Jesus’ statement describes the new relationship we have with His mother as disciples.

Lastly, if one looks through the Old Testament, we see that in the Davidic monarchies the mother of the king was considered the queen of that kingdom. Jesus is the reigning Davidic King, which would make His mother - Mary - the queen.

Thus, you should not feel the least bit defensive when challenged on how much we honor Mary. You are not the one who is out of bounds. How much honor is due to Mary? Going from the Bible alone, we would owe her the honor due to a mother, a martyr, a prophet, a queen.

I was told Mary couldn’t be sinless because she thought Jesus was crazy.
Did she?
by Steve O'Keefe, Staff Apologist

In Catholic and Orthodox circles, the ancient teaching regarding Mary
is that she was preserved from ever committing sin. Among Protestants this is often seen as an absurd proposition. And in response, some will search the New Testament for faults committed by the Blessed Virgin. The example mentioned by your friend is from Mark 3:21. In most English translations, it reads: “Then Jesus entered a house, and again a crowd gathered, so that He and His disciples were not even able to eat. When His family heard about this, they went to take charge of Him, for they said, ‘He is out of his mind.’”

The first thing we need to ask is whether this passage actually portrays Jesus’ family thinking He is crazy. The key phrase “they said”. Who is the word “they” referring to? One could think it refers to Jesus’ family, but there is another option. The next verse says: “The scribes who came down from Jerusalem said, “He is possessed by Beelzebul!” With that in mind, we can propose an alternate reading of Mark 3:21. Jesus’ family isn’t coming to get Him because they think He’d gone mad. Rather, they knew that prominent people from Jerusalem were
accusing Him of being crazy. His family, hearing this, were paying a visit out of concern. Either because they wanted to see for themselves, or because they were afraid of what the scribes might try to do to Him.

But let’s suppose it was Jesus’ family who said He thought He was crazy. The text doesn’t require us to think every member of his family without exception thought this. It could be the majority of the family thought so, and they brought Mary along to prevail upon her son. But all the way there, she could have been saying, “My boy is just fine, you’ll see.

How do I deal with the accusation that Catholics worship Mary?
By Steve O'Keefe, CAA Staff Apologist

There are many ways of dealing with this.  The first way is to point to what the Church officially teaches about the honor we owe to Mary.  The Catechism says: “The Church rightly honors the Blessed Virgin with special devotion.  This devotion differs essentially from the adoration which is given to the incarnate Word and equally to the Father and the Holy Spirit.” [CCC 971].  Regarding our duty to only worship God, the Catechism states: “Idolatry consists in divinizing what is not God. Man commits idolatry whenever he honors and reveres a creature in place of God. Idolatry is a perversion of man's innate religious sense" [CCC 2113-2114].

Now, a Protestant might object that while the Church may officially teach against the worship of Mary, it remains common in the unofficial devotional life of Catholics.  From there I usually ask, “Have you ever met a Catholic who says he believes Mary is God and worships her?”  Pressing this question eventually reveals that your interlocutor has never met a Catholic who actually admits to worshipping Mary.  Rather, he is basing his accusation on his own interpretation of various Marian devotional practices which he thinks constitute worship.  
Now I suggest presenting an analogy.  Suppose there was a person whose culture taught him that giving flowers was always an act of worship.  And now suppose this person observed your Protestant friend laying flowers on his mother’s gravestone.  “Aha!” he says, “You are engaging in ancestor worship!”  Ask your friend how he’d respond to this accusation.  Given time, he’ll eventually explain your point for you.  That is, we can’t cannot presume to know other people’s intentions by interpreting their actions through our cultural lens.  Same goes with Catholic practices of Marian piety.