“Broken” or “Given” in 1 Corinthians 11:24?

Some allege that “broken” creates a theological error since Christ’s bones were not broken. There are two responses to this:

This verse speaks of Christ’s broken body (σῶμα), which was indeed broken, although his bones (οστεων) were not. A body that spills out water from the side truly is a broken body.
“Broken” could refer to Christ’s body represented by the bread, which Christ broke after giving thanks and prior to speaking.

Also, a “broken body” represented by the bread is an apt parallel to the “spilled blood” represented by the cup.