We need to make some serious distinctions in order to tackle this question. I will attempt to make these fairly quickly in a few blog posts.
One of my professors in college (who knew his material so well that he would teach while watching the construction going on outside his window) always used to say, "You must always distinguish." I like that advice.
I don't have a ton of time to research this project, so we'll use Wikipedia. Here is the definition:
A soulmate ( or soul mate) is a person with whom one has a feeling of deep or natural affinity, similarity, love, intimacy, sexuality, spirituality, or compatibility. A related concept is that of the twin flame or twin soul, which is thought to be the ultimate soulmate. In New Age spirituality, the ultimate soulmate is the one and only other half of one's soul. However, not everyone who uses these terms intends them to carry such mystical connotations.
We are each individual, unique, and unrepeatable beings. Bottom line. We each have our own body, our own soul, our own freedom, our own reason. The New Age approach to this, that somebody else actually has the other half of our soul is not consistent with the Church's view of the human person as created by God as a whole person, with deep longings that ultimately find fulfillment in God - not another person.
Now, this is not to say that other people do not shape us or our lives. We are not completely autonomous beings that are untouched or unmoved by the rest of society, friendships and intimate relationships. But,others don't bring pieces of our souls to us, though they may help us realize elements of our being we had not discovered previously.
That is the first distinction I'd like to make. The second is a little simpler.
The idea of a "soul mate" is often popularly thought of in a sentimental light. We want to move beyond the fairy tale feelings, and lovey-dovey stuff here. This is more a change in the way of thinking as we approach the question at hand.