What are the historical arguments against a literal interpretation of Luke 22:44? This question led me to reread Luke 22:44 in various translations, and I noticed that all of them used a comparison, as if Jesus’s sweat was similar to great drops of blood, but not actually great drops of blood. Then I read this commentary:


  Athanasius even goes so far as to pronounce a ban upon those who deny this sweat of blood. 


What arguments was Athanasius fighting against? In addition, what made this issue so significant to Athanasius that he banned the belief outright? As of yet, I’ve been unable to find either his attackers’ arguments or anything from Athanasius himself on the issue. The commentary mentions one “Theophylact”, but I can’t seem to find him either. All Wikipedia had is this list, and all of them lived well after Athanasius.
By historical, do you mean arguments coming from church history aka the early church fathers? 

Just a couple notes: sweating drops of blood is a medical condition called hematidrosis. It is understandable if Jesus did undergo this amount of stress when looking forward to "becoming sin" (2 Corinthians 5:21) and being cursed by God (Galatians 3:13 which references Deuteronomy 21:22-23) and having the wrath of God poured out on him instead of us. We can be confident that it wasn't the physical torture that he would have to endure that caused him duress, as many early Christians were tortured and killed in similar to worse ways (Peter crucified upside-down or another disciple being burned while being crucified) and yet they would be singing hymns approaching their death. Jesus had much much worse to deal with - bearing the sins of the entire world. 

Athanasius is often attributed as being the most important and influential Christian in defense of the Trinitarian conception of God, mostly against Arianism. However, Arianism would have no problem with the drops of blood of Jesus because Arianism believes in the full humanity of Jesus but not the full deity. So, as bradimus commented, it likely was against Docetism, which rejects the full humanity of Jesus. There are all sorts of other heresies in the early church that had to be protected against, such as Nestorianism, modalism/Patripassianism/Sabellianism, Pelagianism, monophysitism, homoiousian (not the name of a heresy but a view of Jesus contrary to homoousian), etc. Very interesting reads. 

Conclusion, Jesus had to be fully God and fully man united in one person, the hypostatic union, or else the atonement fails and should be considered heterodoxy.