This is short one to explain why Christians do not say "Peace be Upon Him" when speaking of Jesus.
God the Word took on human flesh and dwelt among us for this reason:
"Inasmuch as the children have partaken of flesh and blood, He Himself likewise shared in the same, that through death he might destroy him who had the power of death, that is, the devil, and release those who through fear of death were all their lifetime subject o bondage...Therefore, in all things he had to be made like His brethren, that he might be a merciful and faithful high priest in things pertaining to God, to make propitiation for the sins of the people. For in that He Himself has suffered, being tempted, He is able to aid those who are tempted." (Hebrews 2:14-18).
The obedience Jesus showed to the Father when He was on earth, His death on the cross as atonement for our sins, and his resurrection from the dead save us. Therefore, it behooves us to call for His peace on us; not to pretend that we can give our peace to Him.