You have your way.
I have my way.
As for the right way, the correct way, and the only way, it does not exist.
These posts are meant to go over the basics of morality in an easy to understand way. The following is one possible way of how to make sense of morality. I prefer this way because it makes the most sense out of the most facts and has empirical support. If you aren’t familiar with this stuff, it may seem like I am peddling my religion. I am. But if you like to debate, then this stuff is essential.
Philosophy: “It Should Be”
Normative statements: these are prescriptions on what “should be” and can be social norms
- Morality: is about what is “right” or “wrong” and what should and ought to be
- Moral Reasoning: we do this when we reason by using reasons to justify why we are right
We understand morality as being the difference between right and wrong. This definition is an important one, but it leaves things wide open. Moral absolutism only exists if we say it does, but this doesn’t mean that moral relativism is inevitable. I used to listen to Catholic radio, no joke, because I like to dissect arguments; I had such contempt towards their contempt on relativism and still do.
Although I don’t view philosophy as antagonistic to science but rather complementary, moral philosophy is mostly normative, which means that it is a prescription for what is right or wrong. That is for another post. This is from the perspective of an evolutionary biologist. If it doesn’t appeal to you, then you may not be interested in science, which is about what is, not what we want to be.
Science: “What It Is”
Positive Statements: science has the job of describing and not prescribing what is right and wrong
- Morality: is behaviors, thoughts, and feelings that bind us together and makes us care about the wellbeing of others
- but in the right circumstance, we show a preference towards the wellbeing of in-group members
- In-Group: this is a tough one because we can show altruism to strangers; can reciprocal altruism save the day?
- Reciprocal Altruism: we are “moral accountants” and know what we’ve done for others, expecting others to reciprocate
What does the everyday meaning of morality have anything to do with biology? There is a connection because our language is a reflection of what we feel and think. Think about the statement that it is moral to help the weak. This is a normative statement that makes a prescription on what is right, namely to help the weak. We use post-hoc reasoning though because we usually feel first.
We feel that we need to care for others and then we seek reasons to justify it. It usually ends up like, We need to raise the minimum wage because we can’t rely on the free-market. Notice that our moral reasoning “encodes” or hides our thoughts and feelings. That is exactly how biology gets connected to moral reasoning. It must, however, meet the condition of the definition above.
Science on How It Is (iii)
It must meet the condition of the above definition because evolutionary biology only cares about the bottom-line, that is, what helped us in the past to reproduce or survive. There is a problem though because to an evolutionary biologist the selfish person will always outcompete the altruist in an environment of limited resources. So it is perplexing how we could have evolved morality.
Selfishness beats altruism within groups. Altruistic groups beat selfish groups. Everything else is commentary. 
We all know how natural selection works at the level of the individual, but in some cases, it can work at the group-level. That is, traits that helped the group to survive and reproduce when competing with other groups were more likely to be passed on from one generation to the next. Without traits that we link to “goodness” (iv), as described below, the world would be “red in tooth and claw”.
The traits that we associate with evil triumph over the traits that we associate with good within groups, and the counterforce provided by between-group selection is not strong enough to save the day. These are “life’s a bitch and then you die” societies. We would not want to live in them. 
It should be obvious that “binding” with one another and caring about the “wellbeing of others” benefits the group and helps it to survive and compete against other groups. This also explains the propensity to favor in-group members. For those that argue that this reasoning is a priori, I would argue that it was a priori. There is empirical support for group selection occurring in nature (ii), .
i). No, I am not a fan of Nietzsche. This just fits this post and nothing more.
ii) The top-level organization of group selection is what gives harmony to our species because it suppresses self-interest.
Our moral psychology is the societal equivalent of cancer-suppressing mechanisms in multicellular organisms. The coercive side of morality is required to suppress the potential for disruptive self-seeking behaviors within groups. Once the coercive side is established, then it becomes safe for group members to freely help each other without fear of exploitation .
iii) Yes, through the eyes of science, the Nazis in Germany during WWII were behaving morally because they meet the definition of science’s morality. In-group morality is powerful and makes sense out of a lot of things that we label as “evil”. But if you understand the difference between a prescription on morality versus a description, then it becomes an utter waste of time to argue over this. We must create social norms making this immoral. We should seek to understand how we work, so we know what to prevent.
iv) Then how does group selection work if selfish genes prevail within-group selection? I will defer to Wilson:
Between-group selection is strong enough to prevail against within-group selection, favoring the traits that we associate with goodness. Many social species are mosaics of both kinds of traits, some maintained in the population by within-group selection, others by between-group selection.
However, the balance between levels of selection is not static but can itself evolve. In rare cases, mechanisms evolve that largely suppress the potential for disruptive forms of selection within groups, making between-group selection the primary evolutionary force for most traits of the species. Then something magical happens: the group evolves to be so cooperative that it is transformed into a higher-level organism in its own right. 
 Wilson, David Sloan. This View of Life. Knopf Doubleday Publishing Group. Kindle Edition.