You fail to realize that what He said to the Jews next lead them to believe that
He was indeed claiming to be God:
"Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest; because I said, I am the Son of God? If I do not the works of my Father, believe me not. But if I do, though ye believe not me, believe the works: that ye may know, and believe, that the Father is in me, and I in him. Therefore they sought again to take him: but he escaped out of their hand" (Jn.10:36-39).
There can be no doubt in the minds of the Jews who heard Him that He was still claiming to be God, especially when we consider what He told them previously:
"I and my Father are one" (Jn.10:30).
The Jews had also heard Him say that He gives His sheep eternal life:
"My sheep hear my voice, and I know them, and they follow me: And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand" (Jn.10:27-28).
The Jews who heard Him understood that He was claiming to be God and that is why
"they sought again to take Him."
It is also a fact that the reason why the Jews wanted Him put to death was because He
"made Himself the Son of God" (Jn.19:7). They believed when He used the term "Son of God" to describe Himself He was claiming to be God.
If this was just a misunderstanding about what the Lord Jesus meant when He used the term "Son of God" then surely this matter could have been cleared up easily by the Lord just saying that He was not claiming to be God. The fact that He did not say that demonstrates that He was indeed claiming to be God.
Again, earlier when He was accused of making Himself equal to God (Jn.5:18) what He told the Jews only made it even more plain that He was claiming to be God. First, He told them that He had the same power to raise up the dead as does the Father (v.21). He then said that all judgment has been committed to Him (v.22). Then He told them this:
"That all men should honour the Son, even as they honour the Father. He that honoureth not the Son honoureth not the Father which hath sent him" (Jn.5:23).
There can be absolutely no doubt that by those words the Lord Jesus was confirming the Jews' idea that He was making Himself equal to God. And there is no reason at all why He would say those things unless He is God.