Why did the soldiers go backward and fall down when Jesus said "I am he" in John 18:6? I really don't get it. Why did the soldiers trying to arrest Jesus go backward and fall to the ground in John 18:6? Was it because they realized that he was the I AM? If so, then why did they arrest him anyway?
Here are a few commentaries on this verse from Christian Bible scholars. To a large extent, they agree with your suspicion that the men were reacting to Messiah's use of the words "I AM," and the authority with which he spoke them. Parenthetical notes are the original authors'.

From Elliot's commentary for English Readers:


  They went backward, and fell to the ground.—There is nothing in the narrative to suggest that our Lord put forth miraculous power to cause this terror. The impression is rather that it was produced by the majesty of His person, and by the answer which to Jewish ears conveyed the unutterable name, “Jehovah” (I AM). (Comp. Note on John 8:24-25.) Guilt trembled before the calmness of innocence. Man fell to the ground before the presence of God. To Judas the term must have been familiar, and have brought back a past which may well have made him tremble at the present. To the officers the voice came from Him of whom they had been convinced before that “Never man spake like this man” (John 7:46). They have come to take Him by force, but conscience paralyses all their intentions, and they lay helpless before Him. He will surrender Himself because His hour is come (John 17:1); but His life no one taketh from Him. For this sense of awe in the presence of Christ, comp. the account of the cleansing of the Temple in John 2:14 et seq.


From MacLaren's Expositions of the Holy Scriptures:


  ‘I am He!’ When the Band were thus doubly assured by the traitor’s kiss and by His own confession, why did they not lay hands upon Him? There He stood in the midst of them, alone, defenceless; there was nothing to hinder their binding Him on the spot. Instead of that they recoil, and fall in a huddled heap before Him. Some strange awe and terror, of which they themselves could have given no account, was upon their spirits. How came it about? Many things may have conspired to produce it. I am by no means anxious to insist that this was a miracle. Things of the same sort, though much less in degree, have been often enough seen; when some innocent and illustrious victim has for a moment paralysed the hands of his would-be captors and made them feel, though it were but transiently, ‘how awful goodness is.’ There must have been many in that band who had heard Him, though, in the uncertain light of quivering moonbeams and smoking torches, they failed to recognise Him till He spoke. There must have been many more who had heard of Him, and many who suspected that they were about to lay hands on a holy man, perhaps on a prophet. There must have been reluctant tools among the inferiors, and no doubt some among the leaders whoso consciences needed but a touch to be roused to action. To all, His calmness and dignity would appeal, and the manifest freedom from fear or desire to flee would tend to deepen the strange thoughts which began to stir in their hearts.


From Barnes' Notes on the Bible


  hey went backward ... - The cause of their retiring in this manner is not mentioned. Various things might have produced it. The frank, open, and fearless manner in which Jesus addressed them may have convinced them of his innocence, and deterred them from prosecuting their wicked attempt. His disclosure of himself was sudden and unexpected; and while they perhaps anticipated that he would make an effort to escape, they were amazed at his open and bold profession. Their consciences reproved them for their crimes, and probably the firm, decided, and yet mild manner in which Jesus addressed them, the expression of his unequalled power in knowing how to find the way to the consciences of men, made them feel that they were in the presence of more than mortal man. There is no proof that there was here any miraculous power, any mere physical force, and to suppose that there was greatly detracts from the moral sublimity of the scene.


Other commenters give similar commentary. As for your second question, "why did they arrest him anyway?" I'll give another sample from MacLaren, though the emphasis is mine:


  Thus, then, we may see in that picture of our Lord’s surrendering Himself that His trembling disciples might go free, an emblem of what He does for us, in regard to all our foes. He stands between us and them, receives their arrows into His own bosom, and says, ‘Let these go their way.’ God’s law comes with its terrors, with its penalties, to us who have broken it a thousand times. The consciousness of guilt and sin threatens us all more or less, and with varying intensity in different minds.
  He died because He chose; He chose because He loved. His love had to die in order that His death might be our life, and that in it we should find our forgiveness and peace. He stands between our foes and us. No evil can strike us unless it strike Him first. He takes into His own heart the sharpest of all the darts which can pierce ours. He has borne the guilt and punishment of a world’s sin. These solemn penalties have fallen upon Him that we, trusting in Him, ‘may go our way,’ and that there may be ‘no condemnation’ to us if we are in Christ Jesus.


In summary, MacLaren's answer is that they still arrested him because it was his divine will to be arrested in place of his disciples, and also to suffer and die in their place, and indeed in our place.