In John 5:18 the charge against Jesus was that he was calling God His own Father.” Such self-designation was understood to mean “making himself equal with God.”
18 For this reason therefore the Jews were seeking all the more to
kill Him, because He not only was breaking the Sabbath, but also was
calling God His own Father, making Himself equal with God.
Jesus made no effort to deny the charge that he was calling God his own father. On the contrary, he tried to explain the nature of their relationship.
19 Therefore Jesus answered and was saying to them, “Truly, truly, I
say to you, the Son can do nothing of Himself.”
There is more than one way to understand v 19. It could mean that the Son cannot do anything by himself. It could also mean that nothing the Son does is done by himself but always in union with the Father. Jesus’ words in the subsequent text and elsewhere in the gospel of John support both these interpretations.
19 the Son can do nothing of Himself, unless it is something He sees
the Father doing; for whatever the Father does, these things the Son
also does in the same way.
Do not believe me unless I do the works of my Father. 38 But if I
do them, even though you do not believe me, believe the works, that
you may know and understand that the Father is in me, and I in the
Father. – Jn 10:37-38
The words that I say to you I do not speak on My own, but the Father,
as He remains in Me, does His works. – Jn 14:10
Jesus does not claim equality with the Father (cf Phil 2:6). The word equal does not appear anywhere in his response. After all, sons are not said to be the equals of their fathers, but they may be said to be like their fathers. If Jesus is like the Father, it is the Father who has granted him to be so. The Son has life and authority through the Father, and the Father is honored through the Son.
26 For just as the Father has life in Himself, so He gave to the Son
also to have life in Himself; 27 and He gave Him authority to execute
judgment
22 The one who does not honor the Son does not honor the Father who
sent Him.
Rather than an equality, there is a reciprocity between the Father and the Son. Between them is a connection anchored on the one hand by the love of the Father and on the other by the obedience of the Son.
20 For the Father loves the Son and shows Him all things that He
Himself is doing
30 My judgment is righteous, because I do not seek My own will but the
will of Him who sent Me.
What did Jesus’ audience make of his response? While the passage does not say, the charge against Jesus was that he was calling God his own father, a charge that Jesus does not refute. This claim was in and of itself unacceptable to his opponents, regardless of how Jesus might present their relationship. This charge alone would later form the basis of Jesus' conviction.
The Jews answered him, “We have a law, and by that law He ought to
die, because He made Himself out to be the Son of God!” – Jn 19:7