How can Jesus be one Being with the Father when John 17:21-23 teaches that we too are to be one in purpose?
Christians have always held that Jesus is one in purpose with the Father, and they use this John 17:21-23 text in order to demonstrate this point. Obviously the disciples are not one physical body, and they are quite separable (i.e., they exist quite independently of each other). So the best they can be one is in their purpose. Similarly, the Father and Son work in perfect harmony with each other. But Christians also hold that the Father and the Son have a oneness to them that is much deeper than a oneness of purpose. They not only have the same nature, but they make up the same Being.
God is divine by nature (Galatians 4:8), since God has always been God (Psalm 90:2), and is definitely not a man (Hosea 11:9). There is no qualifier here in the Hebrew of Hosea 11:9, so God is not a mere man, a so-so man, a woman, or even an exalted man. He's not a man at all by nature.
Jesus is called "God" in the Bible (Jn. 1:1-3, 14, and 18, 20:28-29, Romans 9:5, Colossians 2:8-9, and Hebrews 1:6-14), so certainly He must at least have God's nature. In other words, He is just as much God as the Father is, and that is why Jesus demands the same honor that the Father gets (Jn. 5:23). So the Father and the Son must have a oneness that is of their very nature. Since LDS give some honor to the Father (like prayer) that they do not give to the Son, they devalue the Son.
Now of course LDS and others will say that Jesus was and is still clearly a man (e.g., 1 Timothy 2:5). But all this shows is that Jesus had another nature as of 2,000 years ago in which He wasn't God. (For more on the two natures of Christ, see my comments on John 10:34.)
The Father and the Son also have a oneness in which they share their very Being eternally. Jesus Himself taught that we were to worship God and serve Him alone (Matthew 4:10). Jesus received worship and commended those who gave it to Him (e.g., Mt. 28:17-20 and Jn. 20:28-29). So Jesus is this "Him" that we are commanded to worship alone. Yet in Jn. 4:23 Jesus says that the true worshippers will worship the Father. So the Father is also this "Him" that we are commanded to worship alone. If the Father and the Son were separate gods who are simply one in purpose and nature, then worshipping both of them would not make any sense according to Mt. 4:10. Further, this "Him" doesn't even know of any other god beside "Him" (Isaiah 40:12-28, 43:10, 44:6, 8, and 24). If Jesus was speaking as Jehovah in these Isaiah passages as LDS like to assert, then why doesn't He know of a separate God on His own team, viz., His Father who is to receive true worship? As a result, it makes a lot more sense, as strange as it may be, to be faithful to what the Bible teaches and hold that the Father and the Son are not only one in purpose and nature, but also in Being.
R. M. Sivulka