Here's my answer to this question. A friend put this in his status and I think it's an excellent thing to dialogue about and open people's eyes to.
If the issue is what makes us "complete", as whole people, then we definitely only need God. Otherwise, "woman" would have been a co-savior with Jesus. Needless to say that's not the case. Being complete is an issue of correcting our sinful condition... not finding personal emotional fulfillment.
But since so many in this day and age confuse being in right standing with God and being personally, emotionally satisfied (which really will never happen here on earth until Christ sets things right, because we're always trying to satisfy ourselves), then yes, some of us need a woman. Some. Some can get by and subdue their passion, while others are designed for marriage. Not everyone can get along like Paul did...
I think we could say that "it's not good for man to be alone" and use the Genesis argument, but we need to pay attention to what Paul said in the New Testament. Jesus came and... kind of changed things. Because what Paul says is that there's nothing inherently bad about being single.
And basically what I mean by Jesus changing things is this... the main goal in Genesis was to populate the earth... there was no fit companion that existed for man. That was not good! So God made woman. But once Jesus came and died and rose, our main objective here on earth was not so much ONLY to multiply, but rather to spread the Gospel. So it doesn't really matter to God whether we marry or whether we go it alone. Because the point of life, now, is growing the Kingdom.
Romance is great! I'm a romantic. But it's just not the main point of us being here... it's not the thing that makes us utterly "complete".
