I think you're making the following claims:
1) What's the point of discussing ethical matters if they're not objective?
2) We can objectively discover what's morally "good".
3) We lose legitimacy making ethical judgments if moral values aren't objective.
(1) There is a lot of value and objectivity in ethical discussions even if there are no objective moral values.
Why would there be no reason to discuss ethics if moral values are subjective? You can discuss all of the factors influencing an ethical judgement with people who don't share your ethical values. You can also change your judgement of an action without changing your ethical values because your understanding of the situation can change.
You are asking whether killing is objectively wrong. This is an incomplete question. What does it even mean to "kill" someone? Stalin's political executions directly killed people, but can we also blame him for the deaths from malnourishment? What if the killing is accidental? When you say that killing is wrong, you have to first define what you even mean. Discussion will help you decide what the ethical value even is.
Secondly, would killing being objectively wrong mean that every action involving killing is wrong? Is it wrong for soldiers to fight in wars? Is it wrong to kill someone in self-defense? What if you only thought it was in self-defense? Every situation is technically unique and *relative* to the situation. Discussion will help you decide which ethical values are involved in each situation.
You can have an objectively wrong ethical judgement of actions even if values are subjective. You can be objectively wrong about the consequences of different actions. You can be objectively wrong in applying your values.
(2) Whether there are objective moral values depends on what you define as a moral value.
Everything I discussed in (1) concerns objective reasons we can base ethical judgements on. Note that everything I discussed were possible contributing factors in our ethical judgment. These are objective outcomes of our actions, and we can legitimately base our ethical judgment on any of these outcomes. These are all statements about what "is" true. When we are making a value judgment though, we are asking what "should" happen.
To make this clearer, let's assume that we can objectively decide which outcomes we "should" aim for. We can objectively say that it's bad when people die, and we can objectively say that it's bad to steal from others. What happens when these values come into conflict? What if someone is going to die if they don't steal food from a shop? You have to compare different ethical values against each other when you decide what "should" happen. Each ethical decision depends on how things are ethically values _relative_ to other ethical values. I can't think of any _absolute_ ethical values because there can always be a more important ethical value.
This is why I don't think we can objectively ethically value things. I don't know of an objective way to compare ethical values. I don't know of an objective way to say you "should" prefer one value over another. You can objectively say this action will result in these outcomes which seem good or bad, but those are also ethical value which also need to be compared to each other. This definition of a moral good, as something you "should" do, makes it incompatible with objectivity to me. We can objectively discover what "is" objectively true about the world because we can observe things which "are". I don't know how to observe what "should" happen, so I have to conclude that values come from us individuals and are thus subjective.
I should note that there are some actions which I think are very obviously bad. We can objectively list all of the bad parts which contribute to the entire action have it be obvious to most people that the action was morally wrong. I'm saying that "obviously bad" is different from "objectively bad", even though they are very close in practice.
(3) You're right that we lose the type of legitimacy which you're arguing for. However, I think that you're making the alternative to objective ethics worse than I think they are.
To start with, where are we using objective ethics? We use ethics to decide how we should behave and how others should behave. What you're saying is that you can tell other people how to behave because there is some objective source of morals backing you up. I can believe there are objectively outcomes of actions which seem bad. But, I don't know what outside of our heads can be telling us what we "should" and "shouldn't" do. Without some external source, it seems like our morals must be internal.
So why do we need to be objectively correct to ethically judge others? I feel okay saying that it seems bad to kill a lot of people unnecessarily and we should try to prevent people from killing others. I don't feel the need to say that killing people is objectively wrong, I feel okay saying it is obviously wrong and we should work together to prevent it. I think that it keeps us humble to realize that we are ultimately the ones deciding the morality of our actions.