If God created angels, He must have had a good reason so how can we object to them existing? ;-)
Angels appear in the Torah, but it seems that the Sadducees objected to the idea of angels:
Now when Paul perceived that one part were Sadducees and the other Pharisees, he cried out in the council, “Brothers, I am a Pharisee, a son of Pharisees. It is with respect to the hope and the resurrection of the dead that I am on trial.” And when he had said this, a dissension arose between the Pharisees and the Sadducees, and the assembly was divided. For the Sadducees say that there is no resurrection, nor angel, nor spirit, but the Pharisees acknowledge them all. Then a great clamor arose, and some of the scribes of the Pharisees' party stood up and contended sharply, “We find nothing wrong in this man. What if a spirit or an angel spoke to him?”—Acts 23:6-9 (ESV)
A careful reading of the passage, indicates that what the Sadducees objected to was not non-human, righteous spirits, but rather the idea that people would become like angels. They didn't believe in life after death, so they didn't believe people were spirits. The Sadducees where wrong about lot's of things, but they were right that people don't become angels when they die.
Many Protestants, especially those who are suspicious of the Charismatic Movement, de-emphasize teaching about angels. Despite a great many mentions of the word in the Bible, there is surprisingly little solid information about angels. We depend on renaissance art and Paradise Lost for much of our popular angelology. Calvin expressed reservations about discussing the topic:
My care, however, must be to keep within the bounds which piety prescribes, lest by indulging in speculations beyond my reach, I bewilder the reader, and lead him away from the simplicity of the faith. And since the Holy Spirit always instructs us in what is useful, but altogether omits, or only touches cursorily on matters which tend little to edification, of all such matters, it certainly is our duty to remain in willing ignorance.—Institutes of the Christian Religion, Book I, Chapter 14, Section 3.