Consciousness. Animals do have an inherent will to live, sure, but there are a lot of animals that willingly commit suicide, either to benefit the whole or due to their own underlying mental illness. A female dolphin who is abused by a pod of male dolphins will sink to the bottom and refuse to breach; likewise a meerkat that is injured and can't escape will give up and allow himself to be eaten to distract. If you try to drown yourself, your body will instinctively thrash, your brain will send chemicals to your sympathetic response, and your body, without consent, will fight to find air. You can't stop this, you can only hinder it, say with chaining yourself down or going too deep. These are 'animalistic' responses that people attribute to a desire to live, but that's not what you're asking, I'm sure. You mean hesitation, right? Why it's hard to just buckle down and get it over with?
Consciousness is a byproduct of that animalistic evolution; you don't need it to live and, in fact, you'd probably be far healthier and happier if you didn't have one, or at least, less of one. It likely came into being from an evolutionary stand-point to make one self-aware. The more self-aware you are, the more you can grow and change to fit adaptability. But like literally everything, too much is a bad thing. Becoming over self-aware, to a point of understanding things we were never meant to understand, backfires, and alerts of how meaningless we are, whether it be a desire to improve the quality of living of the others around us or a recognition that we are wholly insignificant. A dolphin, for example, is also self-aware we have proven and may even have rudimentary consciousness, but a dolphin never looked up at the stars and wondered why it was born or what purpose it has. But it will still fall in love, and when it's love dies, it will kill itself in heartbreak. Even among people, think of how many people go through their lives, vapid, inattentive, never once giving much thought to how the very life they take for granted flies in the face of entropy and is, in terms of physics, transient and cancerous. It's why ignorant people seem so much happier than those suffering; they're unconscientious. How many people have you heard say 'No, don't think like that,' but fail to provide a sufficient reason why. It's always things like 'you only live once' or 'because you're loved' or something else that feels good to say and hear, but doesn't come with a sense of understanding or reasoning for persuading one that their life might be worth living. Understanding yourself, your value, misguided or not, and what death is, what it means, is something worth being scared about. You are programmed to say 'I' and thus you need to know what happens to 'you' when your vessel ceases to exist. Heaven, rebirth, nothingness; those are all beliefs, no matter how much they might seem like truths, and deep down, you know that. And so you're programmed to be scared.
Of course, everyone has their reasons. If you're not philosophical and think that sounds like a bunch of hooplah, then all you really need to know is that we're afraid of death because we know its the end. It's a decision you can't come back from. Everyone is also different, and one who experiences pain in one way may not in another, and you won't know until you try, and that can also be scary. I say a lot I'm not afraid, and I genuinely feel like I'm not, just afraid of the pain. But deep down, even though I know its better for everyone if I go, and even though I've accepted that and it won't stop me when I'm ready, there's still a small nugget of fear about the unknown. Where I'm going, what I'm leaving behind, who I might have been. Doesn't stop me from beating myself up when I chicken out, but I digress.
It's not shameful to be afraid or hesitate. It's a big decision with big consequences and that understanding causes fear.