When you say the "new man" is the Holy Spirit (God), you are in error.
Yes, that would be an error. And I didn't say that.
The "new man" is a completely new creation within the born again believer.
Uh, no.......it's the same 'you', but with a Holy Spirit makeover. You're only new in the sense that you think, act, and look different than you used to. There is no little reneweddaybyday running around inside of reneweddaybyday as if a new little baby got brought home from the hospital the day you got born again for you to google at.
According to 1 Peter 1:3 we have been begotten again
Yes, your body received a spirit, again, the day you were justified, just as you received a spirit the moment you breathed your first on the day of your natural birth. But this time around you received the Holy Spirit. That Spirit birthed a
different you, not an
additional you.
and in vs 23, Peter tells us it is incorruptible seed.
Just because the word of God by which we are born again is incorruptible doesn't mean it can not be uprooted from the soil of one's heart. It was planted and growing in soil #2 in the Parable of the Sower, yet it got uprooted when trouble and trial came around. So we now 'incorruptible' doesn't mean the word can't be uprooted and cast away in unbelief from the person who receives it.
It’s not just the Holy Spirit coming into our "old man", cleaning the "old man" up, and then leaving upon the failure of the "old man"
Right, the Holy Spirit leaves when the person no longer cares about or wants the efficacy of the blood by which he was sanctified, thereby leaving him unprotected for the Day of Judgment (Hebrews 10:26-29). The sin that accompanies such a decision to abandon the protection of Christ's forgiveness is just the result of that decision.