Common arguments in support of the partaking of the divine nature being possible only through Eucharist How do those Christians who believe that believers' partaking of the divine nature that Apostle Peter was talking about in 2 Pet. 1:4 is possible only through Eucharist prove that? What are their main arguments supporting that notion?


  2 Pet 1:4: "Whereby are given unto us exceeding great and precious
  promises: that by these ye might be partakers of the divine nature,
  having escaped the corruption that is in the world through lust."
  (KJV)


I am not sure if the concept of Eucharist being the exclusive way of partaking of the divine nature is a must belief in any one branch of Christianity. It is most likely that in each branch there could be found both proponents and opponents of that belief. However, in my question I am primarily interested in the arguments of RCC, EOC and main-stream Protestants.
In the Catechism of the Catholic Church:


  The Word became flesh to make us "partakers of the divine nature":78
  "For this is why the Word became man, and the Son of God became the
  Son of man: so that man, by entering into communion with the Word and
  thus receiving divine sonship, might become a son of God."79 "For the
  Son of God became man so that we might become God."80 "The
  only-begotten Son of God, wanting to make us sharers in his divinity,
  assumed our nature, so that he, made man, might make men gods."81 CCC 460


"by entering into communion with the Word": since the Word is capitalized, it means the Eucharist.

I think this quote above explains it nicely. I encourage you to read the whole section.