"But he was pierced for our transgressions; he was crushed for our iniquities;
upon him was the chastisement that brought us peace, and with his wounds we are healed."
Bumps, bruises, and bangs, scratches, scrapes, and sprains—all our bodies have been battered to varying degrees. We stub our toes, nick our knuckles, bite our tongues, and throw our backs out of place. For all this, our bodies remain incredibly resilient to the damage done them. Our scars are proofs that we've recovered from many hurts along the way.
My hurts are my hurts, and your hurts are yours. If you break an arm I can "feel your pain" in many metaphorical ways, but my arm will remain unbroken. In like manner, your ability to heal from that fracture will be your own. As healthy and unbroken as my arm is, I cannot transfer any of its wellbeing to you.
As fixed of realities as these are, God chose to get around them one time—not in his favor, but in ours. God chose to reverse the pronouns, so that what was ours is his and what was his is ours. Jesus took upon himself the wounds that we deserve and gave to us the blessings he deserved. His scars are proofs of our healing, as the song says,
"Why should I gain from his reward? I cannot give an answer
But this I know with all my heart his wounds have paid my ransom."