He gives them eternal life because the Father supposedly gave it to him...in other words, it's not something intrinsic in him. That which is divine is perfect (complete) and lacks nothing. Therefore if Jesus had to be "given" and had to be "taught" that makes him less than perfect. Maybe the authors of John believed he was a lesser god, but they made sure no one thought Jesus was equal to the Father in his divinity.
In fact, since you insist on using the Bible (as if it proves anything), perhaps you should know that even Jesus calls the Father his God (Jn. 20:17)! God calling God God? Get real.
In addition to Jesus claiming He would raise Himself up, John 10:22-41 contains His statement that He and the Father are One. They're one person.
BTW, I don't like the version of what's perfect and complete presented. It's contrived, cryptic and can mean anything, as long as it contradicts the evidence.
"you insist on using the Bible (as if it proves anything)
It's a compiliation of evidence.
"God calling God God? Get real."
You complained above that He had not done so. Now you complain, because He did. It's also been noted elsewhere in
Psalm 110:1, The LORD says to my Lord:
“Sit at my right hand
until I make your enemies
a footstool for your feet.”