Did Jesus sin because He allowed himself to be tempted?
To be tempted is not a sin. To give into a temptation is sin. James tells us this in his letter:
James 1:14 But each one is tempted when he is carried away and enticed by his own lust.
James 1:15 Then when lust has conceived, it gives birth to sin; and when sin is accomplished, it brings forth death.
Sin is the result of being carried away by a temptation into lust. Jesus knew the feeling of temptation, as Hebrews testifies, yet He never allowed Himself to be “carried away” into lust and sin.
Hebrews 4:15 For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin.
Jesus paid the penalty for our sin through His death on the cross. But the death that substitutes for us cannot be that of another sinner, since then their death would merely become payment for their own sin. Our propitiation required someone innocent of sin in both behavior and nature – Christ. We recommend you listen to Romans 3B for a full lesson on this important concept.