Here's the NASB*:
"Our old self was crucified with Him, in order that our body of sin might be done away with...."
Let's be honest with the above quote:
What is "our old self" according to the context?
Answer: "our old self" = "our body of sin"
nevermind that you completely ignored the scripture i reminded you of,
but i'm a math guy. so let me stop you right there.
we don't get equality from this verse.
we get:
our body of sin ⊂ our old self
we don't get the reverse; that our old self is a subset of our body of sin. to prove equality, you need both directions.
Romans 7:23-24 also only supports the forward direction:
the law of sin ⊂ our members