And they accused him of slandering/blaspheming God. Wasn't that special?
There are three possibilities, and I'm pretty sure you haven't considered the ramifications of them all, their logical conclusions and how they affect your position.
The first possibility is that Jesus was not blaspheming God (because He was not claiming to be God), and they were simply bearing false witness against Him.
The second possibility is that Jesus WAS blaspheming God by claiming to be God even though He was not, and they were justly accusing Him of such.
The third possibility is that Jesus WAS claiming to be God, and they fully recognized His claim as such, but since they hated Him, they couldn't accept that He was, in fact God, and simply wanted Him dead, and since claiming to be God, according to their laws (they followed the law strictly, almost if not to the point of idolatry of it) doing so was punishable by death by stoning, which they attempted to do multiple times.
The last option you seem to be dismissing without reason.
Questions: Regardless of what the others claimed, was Jesus committing blasphemy by saying the words (and particularly the highlighted portion):
Jesus answered them,
“I told you, and you do not believe. The works that I do in My Father’s name, they bear witness of Me.But you do not believe, because you are not of My sheep, as I said to you.My sheep hear My voice, and I know them, and they follow Me.And I give them eternal life, and they shall never perish; neither shall anyone snatch them out of My hand.My Father, who has given them to Me, is greater than all; and no one is able to snatch them out of My Father’s hand.I and My Father are one.” - John 10:25-30
http://www.biblegateway.com/passage/?search=John10:25-30&version=NKJV
If your answer is "No, by saying the above, Jesus was NOT committing blasphemy," then your only option is to say that they were bearing false witness against Him.
But then you must answer another question:
Was what Jesus said not blasphemy and making Himself out to be God, even though He was a man, because:
A) He was not claiming to be God? OR
B) He WAS claiming to be God because He IS God, and therefore what He said would not be blasphemy?
If your answer is A, then please specify what exactly it was that He said that made them pick up stones to stone Him with, that is NOT inconsistent with the reason they provided, which is (regardless of whether they were lying about it or not):
The Jews answered Him, saying, “For a good work we do not stone You, but
for blasphemy,
and because
You, being a Man, make Yourself God.” - John 10:33
http://www.biblegateway.com/passage/?search=John10:33&version=NKJV
However, if your answer is B, you are no longer consistent with your view that Jesus is not God.
But here is where the real problem for you arises. If you said "Yes, Jesus was committing blasphemy" to my above question 1), you must now establish A) what it was that He said that classifies as blasphemy (and apply this reasoning to ALL of scripture) and B) why it is blasphemy for Him to say it, and 2) you must acknowledge that what His accusers were NOT in fact lying when they accused him of 1) blasphemy and 2) making Himself, a man, to be God, and that would ALSO be contradictory to your position that they are liars.