Oh man, I bloody hate this sort of stuff. My simple answer would be: he didn't have to, he chose to; none of it makes sense unless he chose to freely.
But all that sacrifice/redemption/Adam's sin stuff... TBH I just laugh at it... not meaning to be disrespectful to the people who take it seriously, but it just seems to my mind so... small... as to be quite beneath the general modus operandi of what I understand as God.
For me, 'why he chose to' is 'to show us what it's all about'. The whole crucifixion story is just as powerful and compelling, just as inspiring and real to me, completely divorced from the Judeo-Christian traditions' interpretations of it... I promise you. Yes, I've looked at them in detail, learned in detail about how it fits into that context, but to me it still just isn't something I can take seriously... I have to take it out of that context for it to make any sense to me. But the wider context I see it in is considered heretical and not valid by the majority of people who can even bring themselves to talk about 'Adam's sin'.
IOW I see the whole thing as allegorical. Not the crucifixion itself, but the Judaism-saturated interpretation/context in which say, St Paul places it. If I have to listen to someone presenting me this whole "God had this plan, right..." thing, I'm afraid I find it very hard to keep a straight face.
And I'm a dyed-in-the-wool Catholic (not Roman). And I see no contradiction there.