I will try.
No, the reason Christ died was not to show solidarity with man. The reason He went to that Cross was obedience to the Father and love for mankind.
The "solidarity" refers to two things. First Jesus being the "Son of Man", the "Second Adam", "sharing our infirmitiy", "made flesh", "tempted like us in all points". Second, man must be born again, born from above, made new creations in Christ.
To save us from the bondage of sin and death it was necessary for Christ to come under that bondage as well, to break those chains as one of us so that we could overcome that bondage in Him.
The reason He died was not to show solidarity with man. The reason He died under the powers of Satan was that He was the Son of Man (He was truly man, come under that same bondage).
Think of the Exodus. Consider that Moses could be a type, or foreshadowing, of Christ and Israel's enslavement in Egypt an illustration of man's enslavement to sin and death.
Who was Moses when we first encounter him as a man? He had a high status, raised as an Egyptian in Pharaoh's household. Who was he to the Jews before he joined them? He was above them, an overseer, a member of the ruling race.
Moses not only became one of the Jews he had lorded over, but he became their leader and even to today a symbol of Israel to the Jews.
Once becoming like them, what did Moses do? He lead them out of bondage.