I learned that the song Shalom Aleichem is all about welcoming the Shabbat angels, and clearly angels are celebrated in Judaism. However I've noticed that images of angels are not very widespread in Judaism (at least compared to my impressions of their scope in Christianity). Can someone explain why?
Your father is an outlier. Angels are undisputedly an integral part of Jewish theology.
By way of proof, see Genesis 32:4, in which Jacob sends angels to his brother Esau. Lest you think that "mal'achim" (מלאכים) there means "messengers", Rash"i (the pre-eminent commentary on the 5 Books of Moses) there states clearly, "מלאכים ממש" - real angels. The Torah is replete with other interactions between men and angels, e.g. Abraham (Genesis 18), Lot (Genesis 19), Bil'am (Numbers 22). The list is practically endless.
That answers your first 2 questions. As to the third, there is a specific commandment not to make images of angels in the 10 commandments: "You shall not make yourselves a carved image or any likeness of that which is in the heavens above..." (Exodus 20:4). A "carved image" (פסל) is a 3-dimensional sculpture; a "likeness" (תמונה) is any other representation, including drawings or paintings. That is why you don't find angels represented in Jewish art.
Judaism believes in angels, but one is not permitted to pray to an angel or any intermediary. (According to Rambam and Ramban, praying to angels is idolatrous. Others may be more lenient.) Images of angels may also be problematic in certain cases.
Although "Shalom Alechem" is a widespread custom, there are some people who refrain from saying some (or even all) of it, because it is too close to praying to angels.
There is really no such thing as an icon in Judaism. Icons are objects of veneration in some Christian confessions, especially in Eastern Orthodox Christianity. Judaism, on the other hand, expressly forbids any form of worship of images or statues.
Jews are not forbidden to create images, and angels are present in Jewish art. Such images simply do not play the same role in Judaism, as they do in Christianity.
I notice that you edited your question to remove the point about your father's assertion that Judaism doesn't believe in angels. I think it added an interesting question to the mix. Please allow me some flexibility in answering the questions you posed:
- Why are angels not depicted in Judaism as much as they are in Christianity?
- (This is implied, though not stated) What role, if any, do angels play in Judaism, and does it differ from Christianity's take on the subject?
To answer 1, you can look at any of the answers provided for some idea as to why angels are not depicted very often in Jewish art. I would also posit that it is a cultural difference. Christianity at its core believes in the divinity of a human being (I'm simplifying here, I know, but in some way or another this is the case), whereas Judaism does not. Christianity also supports the idea using icons in worship (crosses, statues, etc.), something that goes against the fundamental core of Jewish belief. Furthermore, much of Jewish art throughout the ages has focused on Jewish life, not religious iconography. Most depictions of the latter tend to be abstract.
To answer 2, angels do play a significant role in Judaism. But what role? The Talmud and the Midrash are replete with stories involving angels, and TaNa"Kh (the Jewish scriptures) has countless references to the Heavens and angels. There are, as others here have noted, some pious leaders who have refused to sing songs or recite religious poems that reference or imply praying to angels, including part of, or all of "Shalom 'Aleichem". The reason that others don't object, however, is that the song does not seek to pray to angels, or even to ask the angels to intercede on our behalf and pray for us to G-d. As a counterpoint, though, the objection may not be the implication of praying to angels but asking the angels to bless us. According to RaSh"I, angels are restricted to performing one task at a given time, which is why three angels visited Avraham (Abraham) and performed the three separate missions described in the ensuing story. Therefore, we cannot ask the angels to bless us if that was not their designated purpose. However, one can also argue that blessing us is their designated purpose, and we are merely asking them to give us a favorable blessing or merely just to bless us as they are supposed to. According to the Talmud, two angels, one good and one bad, accompany a man home from the synagogue on Friday night, and if his home is prepared nicely for Shabbath, the good one wishes for him to have another Shabbath the same way and the bad one answers "Amen"; and if it is not prepared well, the bad one wishes for him to have another Shabbath the same way and the good one answers "Amen". This can be understood as a blessing and a curse, respectively, or they can both be blessings (perhaps one not so pleasant as the other), since even the bad one wishes the man to have another Shabbath, which would imply another week of life. (I don't know of anyone who interprets it that way, though; I'm just suggesting an optimistic outlook on it as I make my next point.) The angels, therefore, are just doing what they are supposed to do, and we are not asking them to deviate from their mission.
As far as I know, though, nobody suggests that we are praying to the angels, nor does anyone suggest that we are asking them to intercede on our behalf. What is suggested by the song is that we are showing the angels how lovely our home is and wonderfully prepared it is (and we are) for Shabbath, so that they can make their assessment and give us the appropriate blessing.
So, in short, we do not see a great many depictions in Jewish art of angels for the many reasons already mentioned, but angels do serve a particularly significant role in Jewish belief.
Not being Christian, I cannot speak from experience as to what Christianity — in any of its variant forms — believes with regard to the role of angels. Being Jewish, however, I think I've explained how we — backed by our traditional sources — relate to them.
Perhaps what your father meant was that Judaism does not believe that the soul of a person becomes an angel after his death, a belief prevalent in other religions. Rather, an angel is G-d's creation through which He interacts with the physical universe.
As to why He created angels, you may open a new question.
I would imagine that the main reason angels do not feature in Jewish art is the difficulty one would have in depicting them. What would one paint or draw? A figure wearing a white dress with wings? How many wings? Are the wings made of feathers, skin or spandex? How many legs does an angle have? Do fire-angles have burning wings, and how do they stop their clothes being burnt?
Without being excessively flippant, Jewish literature is not really all that big on depicting angels, and uses anthropomorphic descriptions in order to describe the indescribable.
It is worth noting that various descriptions of angels in the Torah, such as those that visited Abraham and the one that visited Joshua, depict the angles looking like regular men. So I suppose, if you are painting men, you could be painting angels!
I believe the reason why you don't see as much Jewish art with Angels is because the aesthetic is not as nice.
Jewish Cherub over the ages: As you can see, the angels are mostly animalistic, with very hard to structures. They tend to be chaotic and not very pleasing to the eye.
Christian Cherub: By contrast, Christian art depicts angels as mostly human beings with wings and halo. Very easy to connect to and very yet still be iconic. Also very pleasant to look at.