Calvinism fails when it comes to Christology on this matter. If there is only one will in our salvation (God's) then how to we maintain Christ being consubstantial with all humanity? Was His baptism monergistic, or synergistic? Well, if we maintain Dyothelitism, then we must confess that it is synergistic. Therefore, a Calvinist must deny Christ's consubstantiality. If they decided to opt for the other option and attempt to maintain the consubstantiality of Christ, and assert that Christ's baptism was monergistic, then they would be confessing Monothelitism/Mono-energism.
That is at least why Orthodoxy rejects the Calvinistic view of Monergism. However, there is a slew of other reasons. A couple are:
Total Depravity argues that after the fall our nature became corrupted, and unable to freely choose. This is problematic, since it confuses nature and grace. If the fall from grace was a fall from a good nature into a bad nature, then grace would then be nature itself. This is a Pelagian anthropology, which they get from Augustine (Augustine just took the other side of the spectrum with Pelagius) It also is problematic because it asserts that the cause of sin is a nature issue, not a lack of grace issue (ask any Calvinist "What is grace?") since if sin is present because of a depraved nature, then how do we explain Adam's sin while still having a "good nature"
Limited Atonement is erroneous because it presupposes a Nestorian Christology. Proper Orthodoxy, and logic for that matter, asserts that the Divine Son (person) took on a human nature. Now, persons are not universal, meaning, my person isn't your person (i.e I am Wicket, and my person won't ever be born from a womb again) However, nature is universal, which is why we can study the body and it will be universally true (i.e I have a heart, you have a heart). We participate in the body of Christ, we are the body of Christ, we participate in the Divine nature etc. For the atonoment to be limited, it would have had to have been personal, meaning, Christ would have had to assume another person (i.e Bob?) however, that is a two person Christology, since there would be the Divine Son, and...Bob (?).
Those are just a couple.