The opponents of its use point out two things:
- Ockham was a Latin Nominalist, two things which are Anathema to right-believing and God-fearing Orthodox Christians.
- Ockham's Razor is often used by atheists to "disprove" the existence of God.
For more on Ockham's Razor, see Larry Wasserman.
Edited to add link to post referred to. Also, note that what I said was mildly inaccurate in that the post linked came before the Synod's letter. Read it for yourself if you're interested in the argument.