Then answered Jesus and said unto them, "Verily, verily, I say unto you, The Son can do nothing of Himself, but what He seeth the Father do: for what things soever He doeth, these also doeth the Son likewise.
At first glance it does seem to undermine the truth of the deity of Christ, but when we think carefully and look contextually at the verse it will actually prove it.
Here's a question for you - can you do something of your own initiative and act independently of God? The answer is an obvious yes, of course you can. Every time we sin we are acting according to our own desires and taking our own course. The Lord is saying He could never act independently of His Father - it was impossible for Him to do anything His Father didn't want Him to do. Why is that? Because He is one in nature with the Father.
The Lord had just claimed the prerogatives of God in verse 17 and the Jews got the force of what He was saying:
Therefore the Jews sought the more to kill Him, because He not only had broken the Sabbath, but said also that God was His [own] Father, making Himself equal with God.
John 5:18
The Lord does not back away from saying He is equal with God, but what He is showing is that He is not independent of God. He is not a separate deity in the universe, He is one in nature with the Father, such that He can do nothing independently of Him. Mere men can act in independence of the Father, and do so all the time; mighty angels can act independently of the Father, and have done so in the past; Christ cannot and can never act independently of the Father because They share the very same being and essence.
So rather than this verse attacking the deity of Christ, it affirms it.
