What is the Biblical basis against Melchizedek being the Holy Spirit? A friend of mine is part of a church that teaches that Hebrews 7 indicates that Melchizedek is the Holy Spirit. What are the arguments against this view?

For reference, here is Hebrews 7:15–21 (NIV):


  Jesus Like Melchizedek
  
  15 And what we have said is even more clear if another priest like
  Melchizedek appears,
  16 one who has become a priest not on the basis
  of a regulation as to his ancestry but on the basis of the power of an
  indestructible life.
  17 For it is declared:
  
  
    “You are a priest forever,
        in the order of Melchizedek.”
  
  
  18 The former regulation is set aside because it was weak and useless
  19 (for the law made nothing
  perfect), and a better hope is introduced, by which we draw near to
  God.
  
  20 And it was not without an oath! Others became priests without any
  oath, 21 but he became a priest with an oath when God said to him:
  
  
    “The Lord has sworn
        and will not change his mind:
        ‘You are a priest forever.’”
  


It's also written in Hebrew 7:3 (KJV),


  Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.


I am a bit confused here. Anbody?
The Book of Hebrews speaks of Melchisedec 9 times (5:6,10; 6:20; 7:1,10,11,15,17,21) and in each case it is to inform us that Jesus is made a priest in the order of Melchisedec. The theology of Hebrews is strange, but no more so than in its portrayal of Jesus as a priest in the order of Melchisedec. The filioque clause that now forms part of the Nicene Creed, states that the Holy Spirit comes from the Father and from the Son [Jesus]. I think this clause requires some serious mental gymnastics to read from Hebrews that Melchisedec is the Holy Spirit.

Melchisedec is first mentioned in Genesis 14:18, where he is the King of Salem and priest of the most high God. Again, it is not traditional to think of the Holy Spirit, the third person of the Trinity, as merely a priest of God. Melchisedec can not be the Holy Spirit.

Hebrews 7:3 speaks of Melchisedec in terms that could at first read like divinity: without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God.  The NAB footnote to this passge explains:


  4 ... this is perhaps a quotation from a hymn about Melchizedek. The rabbis maintained that anything not mentioned in the Torah does not exist. Consequently, since the Old Testament nowhere mentions Melchizedek's ancestry, birth, or death, the conclusion can be drawn that he remains . . . forever.