It's dangerous, plain and simple
One thing we know, it sure as heck is never healthy.
You can’t live without air, food and water. That’s it. Love interests, however, are in another category altogether. While that person may be a fun, fantastic partner or your soul-mate, or a dear, dear relative, endowing them or the relationship with that much power over your own life and the thought of "I can't live without you", is dangerous, and here’s why:
No One -- outside of Yourself -- can make life worth living. There is no person in this Universe so wonderful and awesome, so magnificent, that life is not worth living without their presence. Yes, if they leave you’ll miss them terribly, but it need not be a life-altering moment.
Think of it this way: life is an adventure, it’s a journey we each take to bring us into self-truth and an understanding of our own souls. Most people come into your life for a season (days, months, years) and with a purpose - a lesson - primarily to teach us something we need to know. When their job is finished, they leave in some manner or another. Some teach us how to love and how not to love, how to grow and how not to grow; and it is dependent upon us to grasp what the lesson is and apply it from then on.
When you think along those lines of "I can't live without you" you’re belittling yourself. And, if you’re belittling yourself, how can you genuinely love someone else? You can only love another to the degree you first love yourself. You’re basically telling the Universe it did a lousy job in creating you, it made a ton of mistakes, and didn’t know what the heck it was doing. You’re telling the world that without So-and-So, you’re worthless and you have nothing to offer humanity. Not one person has ever entered this earth realm without something to offer. We all come bearing gifts. The conundrum is knowing how to put those gifts to their best use in service of others.
These thoughts suggest a dependent personality. Constantly depending upon another for your joy, your well-being or satisfaction causes self-doubt and it will cause great disappointment when you come to a spot of realization that another cannot “give” you what you can already give yourself. Ceding responsibility of your life to another and relinquishing your own power is unhealthy and a great way to become a door-mat.
Thinking "I can't live wihtout you" also veers into obsessive behavior. By all means, ask yourself what lengths you’re willing to go to keep this person by your side. If the answer is “anything necessary,” then consider seeking professional help to overcome these feelings. Obsessing over someone, seeking their approval over all things, instead of trusting your own feelings and intuition is hazardous to your mental stability.
When your thoughts are consumed with the presence of someone else, you fail to appreciate other interests in life, and you may very well fail to recognize your loved one’s failings and faults and give them a pass on any negative behavior. You can easily make this person “God” in your life, bestowing upon them your own form of idol worship.
Again, try understanding that you and you alone have all the power necessary to bring about a fulfilling life, a life worthy of living. The very fact that you’re here heralds your worthiness. How you live this life is up to you. With or without anyone in your life, you’re still a powerful, vibrant being who can change and rearrange any aspect of your life you want.