Why does the Holy Spirit not take the form of a human being just like Jesus did? The Holy Spirit in the Bible takes the form of:
Dove, Oil, Light, Wind and Tongues of Fire. But never a human being. Why?
According to Trinity theology, there are three persons in God and they are one. 


  
  Father
  The Word or the Son
  Holy Spirit
  


They are all spirit according to John 4:24.


  God is spirit, and his worshipers must worship in the Spirit and in truth." (John 4:24, NIV)


Though there are three persons, only one of them took the form of flesh. 


  The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the
  Father, full of grace and truth. (John 1:14, NIV)


The Bible doesn't tell us whether all three of them can become flesh, but there is no reason why they cannot do so, because God is All-powerful. All we know is that only The Word became flesh and is called the Son of God. There is a strong reason why The Word became flesh and it was a necessity. It was all planned by God that His Son should become human and die on the Cross. It was the will of the Father that the Son should born from a woman and die for all mankind. Since it was necessary for the Son to die as human on the cross, the Son/Word became flesh.


  All inhabitants of the earth will worship the beast--all whose names
  have not been written in the Lamb's book of life, the Lamb who was
  slain from the creation of the world. (Revelation 13:8, NIV)
  
  Praise be to the God and Father of our Lord Jesus Christ, who has
  blessed us in the heavenly realms with every spiritual blessing in
  Christ. For he chose us in him before the creation of the world to
  be holy and blameless in his sight. In love he predestined us for
  adoption to sonship through Jesus Christ, in accordance with his
  pleasure and will— to the praise of his glorious grace, which he has
  freely given us in the One he loves. (Ephesians 1:3-6, NIV)


The three persons in the Trinity have different roles. The Father plays the role of a father, the Son plays the role of intercession between God and men, the Holy Spirit dwells inside the believers and help them to live a holy life.


  But the Advocate, the Holy Spirit, whom the Father will send in my
  name, will teach you all things and will remind you of everything I
  have said to you. (John 14:26, NIV)
  
  But very truly I tell you, it is for your good that I am going away.
  Unless I go away, the Advocate will not come to you; but if I go, I
  will send him to you. When he comes, he will prove the world to be in
  the wrong about sin and righteousness and judgment (John 16:7-8, NIV)


God can live inside the believers in the form of the Holy Spirit. Though the Father and the Son are in Heaven, the Holy Spirit is in this world to help the believers.


  Do you not know that you are God’s temple and that God’s Spirit dwells in you? (1 Corinthians 3:16, ESV)