1. Robert M. Seltzer, Jewish People, Jewish Thought: The Jewish Experience in History (New York: MacMillan, 1980) 242.
The first century C.E. Roman historian Tacitus states regarding the Jews, “They hold it to be impious to make idols of imperishable materials in the likeness of man; for them the Most High and Eternal cannot be portrayed by human hands and will never pass away…”
I wonder why Judaism opposed representing God through images. Maybe the feeling was that depicting God limited him, or brought him down to the level of whatever was used to represent him, be it human or animal. Paul, after all, criticized the Gentiles because they “exchanged the glory of the immortal God for images resembling a mortal human being or birds or four-footed animals or reptiles” (NRSV). This echoes Psalm 106:20: “They exchanged the glory of God for the image of an ox that eats grass.”
Philo of Alexandria (first century C.E.) says in Special Laws 1:8:41 that God is invisible and can be perceived only by the purest intellect. This echoes Platonism, which elevated the unseen world of the Forms (Ideas) above the world that we can see. For Philo (perhaps), and, in a sense, for certain biblical writings (e.g., Deuteronomy 4:12), we should not try to limit God through a visual representation of him, for we know God by contemplating what God is all about: his attributes, his actions, his commandments, his character.
According to the Jewish Encyclopedia’s article on “Anthropomorphism,” (see Earlier Rabbinical Literature), the rabbis struggled with the anthropomorphic depictions of God in the Bible:
In the older rabbinical literature there also occur a number of utterances which show a tendency to suppress low and sensuous conceptions of God by means of a new hermeneutics. Referring to the fanciful and figurative expressions of the Prophets, an old rabbinical saying remarks: “The Prophets show great daring in likening the Creator to the creature,” (Gen. R. xxvii. 1). Rabbi Akiba sought a different interpretation of those passages in the Bible that seem to identify God and the angels. God, in His sublimity, must in His very essence differ from His holy angels. Compare Mek., Beshallaḥ, 6, where Akiba declares as heretical the certainly ancient explanation of the words “like one of us” (Gen. iii. 22) as referring to the angels. Compare his Christian contemporary Justin Martyr, who declares the interpretation Akiba rejected to be “Jewish heresy” (”Dialogus cum Tryphone,” 62) Whenever actions similar to those of a human being are predicated of God, the older rabbis employed the term 
(”as though it were possible”); intending by this term to say that these expressions are not to be taken literally, but only as a mode of speech accommodated to the average intellect (Mek., Yithro, 4).
According to this article, the rabbis didn’t want to reduce God to the level of his creation.
Are there ways that we reduce God to something lower than he really is?
2. Geza Vermes, Scripture and Tradition in Judaism (Leiden: E.J. Brill, 1961) 211.
According to ancient Jewish theology, the atoning efficacy of the Tamid offering, of all the sacrifices in which a lamb was immolated, and perhaps, basically, of all expiatory sacrifice irrespective of the nature of the victim, depended upon the virtue of the Akedah [(Abraham's near-sacrifice of Isaac)], the self-offering of that Lamb [(Isaac)] whom God had recognized as the perfect victim of the perfect burnt offering.
Vermes documents that there were ancient Jewish traditions asserting that God accepted Israel’s atonement offerings on account of the merit of Abraham and Isaac at the Akedah (Genesis 22). This interested me because it somewhat reminded me of Hebrew 10:4’s statement that “it is impossible for the blood of bulls and goats to take away sins.” According to many Christians, Hebrews is saying that animal sacrifices were not sufficient to atone for sin, but they were efficacious in Old Testament times because God retroactively applied to the Israelites the saving blood of Christ. Could we see something similar in Jewish tradition: that animal sacrifices are not enough to atone for sin, but they work because of something else, namely, the merit of Abraham and Isaac at the Akedah?