the importance of the Council of Chalcedon

https://en.wikipedia.org/wiki/Council_of_Chalcedon

https://www.gci.org/history/chalcedon

https://orthodoxwiki.org/Fourth_Ecumenical_Council

Essentially, the Council of Chalcedon rejected Eutychianism, a variant of
Apollinarianism (which has NOTHING to do with traducianism except
inasmuch as it may misinterpret or misapply it, unlike the rash statements
of a proabortion video that pretends that anti abortionism partakes of the
Apollinarian heresy). Both in slightly different ways claimed that Jesus
Christ was essentially divine only, and that His humanity was swallowed
up in the ocean of His divinity so irrelevant at best (Eutychianism).

Like most if not all heresies, the origin was either clerical or monastic, the
latter in Eutyche's case, so much for fasting and prayer automatically
making you a good theologian.

The tendency semiconsciously to view Christ as divine only and lacking
much if not all humanity, is the sole reason that alledged proofs of His
having been married and maybe had children (false) are treated as
in some way disproving His divinity, the assumption being that anything
that showed He is human disproves His divinity. (ignored of course is the
issue of His dying on the Cross or suffering from flogging and nailing
or mention of His being hungry or tired or sleeping.)

The fact is, that since Jesus is both 100% divine AND 100% human,
IF He had married and had children such events would be totally
irrelevant. (There is no reason to believe they are true and always hail
from weird agendas and fraudulent "gospels" of much later origin than
the eyewitness Four Gospel of the New Testament. Indeed, knowing He
would not remain on earth long enough to be a good husband and father
He might well have deemed it unfair to use this option. It could also
interfere with His mission when it would start, so His wife and children
would effectively have to be abandoned if they didn't trail along with Him.
And maintaining celibacy was a good example anyway of self control
not only of bodily desires but of emotional needs.)

Chacedon is rejected by the monophysites, who range from really
monophysite similar to Eutychianism to miaphysite which is monophysitism
lite and tends to claim it is misunderstood. Both sides accept the Nicene
Creed, that He became flesh, but seem to understand it somewhat
differently. Using what he thought was from Athanasius but actually from
Apollinaris, St. Cyril of Alexandria had used the formula one divine nature
incarnate to answer Nestorius who divided the two natures too much.
But the interpretation that this means there is one emulsified combined
nature after the Incarnation that involves modification of both the divine
and human so that it is not really either anymore, is hardly what St. Cyril
was driving at and makes contrary statements here and there, but his focus was
on the excessive dividing of the natures so often sounded monophysite.

Chalcedon made sure its dogma matched that of St. Cyril who the monophysites
also claim. Monophysitism was also fuelled in part by politics, wanting to
use this religious variation to escape the control of the Byzantine emperor.

the Monophysites rejected Eutyches ALSO before long. so the end result is
closer to Orthodoxy.

Often their supporters quote St. John of Damascus who said they are Orthodox
in all ways but leave out that he said "EXCEPT" in this matter of their ideas
about the human and divine natures of Christ.

Also a problem is that the Greek language was evolving, so that physis and
hypostasis and so forth had more than one meaning. Likely many miaphysites
hold an Orthodox view but think they don't others don't and pretend they do.
Miracles and so forth are reported among them. One Orthodox writer considered
their Eucharist is valid, but because they partake of it in a state of sin (heresy)
it causes their souls harm or stores up wrath for them in the Judgement, rather
than being salvific.

The importance of Chalcedon is precisely that it declares that Christ is both
fully human and fully divine, refuting ahead of time some new agey notions
about Christ, and ruling out the use of either evidences of humanity or evidences
of divinity as proof against the Orthodox (or Roman Catholic or original
mainline protestant) Christology.

A subclinical Marcionism (denial of the Father being good and drawing a distinction
between "the God of the Old Testament" dismissed as petty and tribal and "the God
of the New Testament") and a subclinical monophysitism seems to exist in the
mentality of many protestants in America at least for many generations.