This is the instruction of the Buddhas.
And we have to approach these three things in this specific order.
We cannot make progress on the path without first avoiding harming others. We cannot purify the mind, without first doing the other two.
There are various ways of looking at avoiding harm, depending on where we ‘find ourselves’ right now. For some, it may simply mean that we will not kill other sentient beings. For others it may mean that we do not eat animal flesh of any kind. For yet others it may mean that we avoid eating meat, fish, foul on a certain day of the week.
Little steps in the right direction is wonderful!
Like the body is one interconnected organism, so is all of nature. What affects one, affects all.