Why would orthodox Christians consider Christian Science unorthodox if it essentially a mix of Augustine and healing?

Christian Science contains elements of four heresies that were condemned in the early Church, especially gnosticism:

• Gnosticism: the denial and/or denigration of the material world

There is no life, truth, intelligence, nor substance in matter. All is infinite Mind and its infinite manifestation, for God is All-in-all. Spirit is immortal Truth; matter is mortal error. Spirit is the real and eternal; matter is the unreal and temporal. Spirit is God, and man is His image and likeness. Therefore man is not material; he is spiritual. (Mary Baker Eddy, Science and Health, 468)

• Nestorianism: a disjunction between Jesus the man and Christ the Son of God
• Modalism: a denial of the Trinity
• Peneumatomachianism: a denial of the divinity of the Holy Spirit

I will enumerate all of Mr. G.K. Chesterton's (the man who wrote the book on Orthodoxy) differences here:

It is a "purely spiritual" form of Christianity.

the essential difference between Mrs. Eddy's creed and mine is that she anchors in the air, while I put an anchor where the groping race of men have generally put it, in the ground.

FAITH HEALING AND MEDICINE By G. K. Chesterton From the column Our Note Book, The Illustrated London News. October 22, 1910

And, like the gnostics of the first and second century:

In short, the first and last blunder of Christian Science is that it is a religion claiming to be purely spiritual. Now, being purely spiritual is opposed to the very essence of religion. All religions, high and low, true and false, have always had one enemy, which is the purely spiritual.

ibid

And the Manichaens who came after - and Augustine firmly opposed (after converting to Catholicism from the faith):

Christian Science may or may not start with the assumption that God is in his heaven and all is right with the world; it is a subject for a respectful debate with Christian Scientists. But Christianity emphatically began with the assumptions that God is in his heaven and all is wrong with the world; and from those two things the whole Christian theory proceeds.

BROWNING AND THE AMERICAN OPTIMISTS - By G. K. Chesterton From the column Our Note Book The Illustrated London News November 22, 1930

It denies death (all death including the part of the Creed where we say "Jesus died and was buried"

Should we passionately asseverate that something was as true as death, even if we all joined the religion of some Mrs. Eddy, which declared that death is a delusion, imposed by a conspiracy of undertakers?

THE DESTRUCTION OF LIBERTY - By G. K. Chesterton From the column Our Note Book The Illustrated London News October 06, 1934

And, while not a part of the faith, it denies human reason in the sciences, which is what Pope John Paul II would call fideism the twin heresy of rationalism.

The very system which would deny and destroy all physiological science, all medical science, all anatomical and surgical science, still calls itself Christian Science.

SCIENCE AND THE DRIFT TO SUPERSTITION - By G. K. Chesterton From the column Our Note Book The Illustrated London News November 13, 1920

As well as the twin heresy of materialism.

For the Hygienist is urging that if you take care of the body the soul will benefit by it; while the Christian Scientist is urging that if you take care of the soul the body will take care of itself

THE CRANKS OF THE HIGHER THOUGHT - By G. K. Chesterton From the column Our Note Book The Illustrated London News August 15, 1914

And, frankly, it is wrong to categorically deprive sick people of help

I think it both crazy and cruel for a follower of Mrs. Eddy to seek to deprive the sick of the help of any science except Christian Science

THE RAILS OF REALITY - By G. K. Chesterton From the column Our Note Book The Illustrated London News January 26, 1918

So, there are probably more instances of GKC's arguments against Christian Science, but this probably suffices. He was not a fan.

This quote from catholic.com sums up why a Catholic group considers it unorthodox pretty well:

Christian Science purports to be a Christian organization. It borrows heavily from the Christian vocabulary but denies all the fundamental Christian dogmas. It rejects the belief in a personal God, the Trinity, the divinity of Christ, the existence of sin and the devil, the Resurrection, and heaven and hell.

In short, Christian Science denies the fundamentals of the faith. This is how heresy is defined. It has nothing to do with having ideas similar to other Christian writers.

Mary Baker Eddy (Catholic Answers)

Want more details? Mary Baker Eddy's full teachings are found in her book, now online, Science and Health, with Keys to the Scriptures. Here are several extracts with links. As you can see, Mary uses the same terms as the Bible does, but reinterprets them.

25:3-9 tells us that Christ's blood did not cleanse us from sin on the cross:

The efficacy of Jesus’ spiritual offering is infinitely greater than True flesh and bloodcan be expressed by our sense of human blood. The material blood of Jesus was no more efficacious to cleanse from sin when it was shed upon “the accursed tree,” than when it was flowing in his veins as he went daily about his Father’s business.

from http://www.christianscience.com/the-christian-science-pastor/science-and-health/chapter-ii-atonement-and-eucharist?citation=SH%2025:3-25:12

361:1-3 tells us that Christ is not really God Himself, but only an idea of God:

The Jew believes that the Messiah or Christ has not yet come; the Christian believes that Christ is God. Here Christian Science intervenes, explains these doctrinal points, cancels the disagreement, and settles the question. Christ, as the true spiritual idea, is the ideal of God now and forever, here and everywhere.

from http://www.christianscience.com/the-christian-science-pastor/science-and-health/chapter-xi-some-objections-answered

335:24-30 Tells us that sin and sickness are not real:

XX. Mind is the divine Principle, Love, and can produce nothing unlike the eternal Father-Mother, God. The one divine Mind Reality is spiritual, harmonious, immutable, immortal, divine, eternal. Nothing unspiritual can be real, harmonious, or eternal. Sin, sickness, and mortality are the suppositional antipodes of Spirit, and must be contradictions of reality.

from http://www.christianscience.com/the-christian-science-pastor/science-and-health/chapter-x-science-of-being

30:3-12 tells us that Jesus and the Christ were separate entities. Also, He was a way-shower, and not the way Himself:

Born of a woman, Jesus’ advent in the flesh partook partly of Mary’s earthly condition, although he was endowed with the Christ, the divine Spirit, without measure. This accounts for his struggles in Gethsemane and on Calvary, and this enabled him to be the mediator, or way-shower, between God and men. Had his origin and birth been wholly apart from mortal usage, Jesus would not have been appreciable to mortal mind as “the way.”

from http://www.christianscience.com/the-christian-science-pastor/science-and-health/chapter-ii-atonement-and-eucharist?citation=SH%2030:5-30:13