Why doesn't 1 Timothy 5:21 indicate that angels are part of the Godhead? I was doing a little historical reading, and I read a little John Biddle (an English Unitarian).  He makes the argument that the phrase "in the name of the Father, of the Son, and of the Holy Ghost" in the great commission (Matt 28:19) doesn't prove that the Father, Son, and Holy Ghost are three Persons in one God, since a similar phrase is used in scripture but saying "elect angels" rather than "Holy Ghost," and that nobody would dare suggest that angels are part of the Godhead:


  1 Timothy 5:21 (KJV) I charge thee before God, and the Lord Jesus Christ, and the elect angels,...


(Despite his argument, I actually knew a guy at my last church who did argue that the angels are part of the Godhead, but that's neither here nor there.)  

So my question is, how do orthodox Trinitarians explain the difference between the formula of "Father, Son, Holy Ghost" and why that formula is taken to mean that God subsists in three Persons, whereas the formula "God, Jesus Christ, Elect Angels" is not taken to mean that angels are Persons of the Godhead?
Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, (Matthew 28:19, NIV)
I charge you, in the sight of God and Christ Jesus and the elect angels, to keep these instructions without partiality, and to do nothing out of favoritism. (1 Timothy 5:21, NIV)

The core difference is those two emphasised words. Matthew 28:19 is asserting that the three persons of the Father, the Son and the Holy Spirit have one name — one reputation, one identity. The way you share your name with your spouse or family, showing your close united relationship, is a little bit like the way that the persons of the godhead share a name. 1 Timothy 5:21 merely says that they are all in the one place watching us, without suggesting any kind of unity.
(The word translated sight in 1 Tim 5:21 is ἐνώπιον enopion.)