No born Catholic can really understand this issue, because they were not steeped in it from a very early age.
Most (not all, but most) Protestant Churches do not pray to Saints at all (some either do not recognize Saints, or they acknowledge the Apostles, and St. Paul, but that’s about it).
They do not believe that anyone, at any time, interceeds between you and God. That no one that is not living CAN ask God to forgive you, and that even a living person really has little if any influence on God. It is YOUR petition to God that matters, and YOUR asking for forgiveness.
There is no requirement to confess to any human being, all you need to do is to confess to God and ask for forgiveness for your sins.
Therefore, the very concept that anyone would pray to any person OTHER than God appears to them to be a form of worship. They can not understand even the concept that you would ask Mary (or Peter, or John or anyone else) to pray to God and ask that you be forgiven, cured, your mother cured, etc., etc.
To them, miracles happen solely because GOD decided to pass a miracle, and no intercession by anyone else had anything at all to do with this.
Therefore, paces like Lourdes, Fatima, etc., to them are nothing more than Churches worshiping Mary. They have nothing to do with God, they are set up to deify Mary (or St. James, St. Christopher or whoever that church is named for, dedicated to, etc.).
The Ten Commandments specifically outlaw any “Graven Image”. To them, statues of Jesus, Mary, etc. are nothing BUT Graven Images. The same is true of pictorial windows, and much of Church Art. To them, out insistence on having such things is nothing more than a total and complete display of just how far from Christianity the Catholic Church has really strayed.
I grew up in one of those types of Protestant Churches. We were taught that the Catholics, Episcopalians, Lutherans, etc. were ALL false churches (THE CATHOLICS WERE THE ABSOLUTE WORST OF THE LOT. THEY WERE DIRECTLY LED BY THE DEVIL INCARNATE ON EARTH, THE POPE!).
I had a difficult time with statues especially when I first came into the Church. I had a hard time with the Rosary, the Hail Mary, Novenas to the Blessed Mother, etc. It took a LONG time (long after I had decided to become a Catholic) before i was truly comfortable with those kinds of things.
You will NEVER convince a rock hard Protestant of that stripe that you are NOT worshiping Mary. They look at this from such a totally different viewpoint, that Catholics essentially can not even speak the same language to them. Whatever you do say will essentially be considered to be a bunch of lies anyway.