I only hope I can give half as good an answer.
Let's start with the "random" issue. If life is a product of pure randomness, then it is infinitely rare. (The probability of life is extremely small, in comparison to any other event, statistically-speaking.) Thus, to extinguish such a life is to destroy one of the rarest, scarcest possible combination of events.
In fact, we can add some other elements here, depending on the exact nature of the belief.
First, if the person speaking believes in a totally deterministic universe, then he must ALSO believe that the person who has been "convicted" had no alternative. The events were already pre-determined. As such, if anything should be tried, it should be the events, not the person subject to them.
Second, if you allow for free-will, but believe in the concepts that the market economy esposes, then you believe that value is a direct function of rarity. Thus, as life is rare, life must also be valuable. If you would not break anything else of comparable value, for ANY reason, then to break a life must be (by that reasoning) equally unacceptable.
Ok, now we'll move onto evolution. This is a good one to argue from, as (scientifically speaking) there is no serious question that evolution is the correct hypothesis.
Evolution argues from two standpoints. First, it argues that an organism will always tend to evolve to suit the conditions it is in. (Note that this is NOT the same as arguing that the organism will always get more complex, or more "advanced". If conditions favour simplicity, then the "fittest" to survive will be the simplest.)
It also argues that there will always be a combination of evolutionary pressures - the physical environmnent, and other occupents within that environment. That organisms compete for resources, between any group and between groups, where those resources are controlled by the environment in which they co-exist.
Evolution dictates that certain "morals" must exist within all creatures capable of posessing them, where such morals offer an evolutionary edge. As such, where such an edge can be demonstrated, those morals must exist, regardless of whether we can directly perceive them or not.
Let's take some examples, here. Do dogs posess morals? The answer must be yes. When you are a single member of a collective, personal advantage is always superceded by the advantage of that collective. For example, obedience to the pack leader, sharing food, etc, will create personal advantages BECAUSE the individual has placed the collective first.
Dolphins, if threatened by sharks, will often counter-attack, even though (individually) that is near-suicide. (In fact, it usually IS suicide. Dolphins vs sharks is NOT favourable to the dolphin.) However, two dolphins charging a shark, in opposite directions, impacting the gills, will kill the shark. Where the pod's survival depends upon removal of the shark, they will do this, regardless of personal risk.
Lastly, "animals have no problem with hunting and killing". That is true. An, yes, this often involves "getting rid of the weak". That's because, in the environment they live in, the weak are a serious threat to the well-being of the group and of the environment.
When animals kill weaker prey, for food, they are preserving the health of the stock of their prey. Failure to do so could cost them that stock, altogether, and thereby their own existance.
IMHO, that kind of structured thinking and preservation of something outside the individual defines the very essence of "morality".
Oh, and a "higher power" isn't restricted to a deity. If you believe in the laws in the land you live in, then you believe that those who made those laws were a power greater than yourself.
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