Many people would claim that "life" is another designation for Jesus because Jesus said:

"I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst." -- John 6:35 (ESV)

and

“I am the resurrection and the life. Whoever believes in me, though he die, yet shall he live, and everyone who lives and believes in me shall never die. Do you believe this?” -- John 11:25-26 (ESV)

and

“I am... the life. No one comes to the Father except through me.” -- John 14:6 (ESV)

and then when John testifies:

All things were made by Him; and without Him was not any thing made that was made. In Him was life; and the life was the light of men. -- John 1:4 (ESV)

"Him" in John 1:4 obviously refer to the origin of life which could only be God. Then people would use this verse correlate Jesus with God and come to the assumption that Jesus who called himself "life" should be God Himself. However, John as the author of the same book of the above quotes, recorded these words which Jesus himself said:

For as the Father raises the dead and gives them life, so also the Son gives life to whom he will. For the Father judges no one, but has given all judgment to the Son, that all may honor the Son, just as they honor the Father. Whoever does not honor the Son does not honor the Father who sent him. Truly, truly, I say to you, whoever hears my word and believes Him (the Father) who sent me (the Son) has eternal life.

He does not come into judgment, but has passed from death to life.

Truly, truly, I say to you, an hour is coming, and is now here, when the dead will hear the voice of the Son of God, and those who hear will live. For as the Father has life in himself, so He has granted the Son also to have life in himself.

-- John 5:21-26 (ESV)

This means that according to both John and Jesus that the Father is actually the source of life. Whenever Jesus calls himself "the life", "I am the light", he states that he is the means ("the way" according to John 14:6) to "the life" or "the light" of the Father. "The way" he is "light" or "life" is by testimonies, demonstration, guidance or teachings of the Father. Likewise, Jesus encouraged his disciples to be the same to the lost who are deceived by the darkness so that they too may have "eternal life".

And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up: That whosoever believeth in him should not perish, but have eternal life.

For God so loved the world, that He gave His only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
For God sent not His Son into the world to condemn the world; but that the world through him might be saved.

-- John 3:14-17 (KJV)

Whoever believes in the Son has eternal life; whoever does not obey the Son shall not see life, but the wrath of God remains on him. -- John 3:36 (ESV)

Jesus said to her, “Everyone who drinks of this water will be thirsty again, but whoever drinks of the water that I will give him will never be thirsty again. The water that I will give him will become min him a spring of water welling up to eternal life.” -- John 4:13-14 (ESV)

The thief comes only to steal and kill and destroy. I came that they may have life and have it abundantly. -- John 10:10 (ESV)

Whoever has the Son has life; whoever does not have the Son of God does not have life. -- 1 John 5:12 (ESV)

Therefore, Jesus had said:

“I am the way, and the truth, and the life. No one comes to the Father except through me.” -- John 14:6 (ESV)