I'm not a settler, settlement advocate or anything of the sort (the polar opposite, actually) - but I have had the extremely questionable pleasure of having come in contact with the more militant end of West Bank settlers more than once.
The way they explained what they were doing to be basically boils down to "the land is ours, so this is where we ought to be".
For a lot of the more extreme types, there are religious aspects to why they think this - but I have, in fact, come across reasonably "secular" arguments a couple of times, too.
Underlying all of it, in my personal experience but also from what I have read, the basic, underlying premise is simply "we have more of a legitimate claim to the land than they do". Underpinning this, you'll then find all sorts of arguments, ranging from the comparatively benign claim that there is simply no such thing as a unique Palestinian identity and "why don't they just move across the river where their kind live?" (which, just to be clear, is an insane mentality and the rhetoric of ethnic cleansing; I say "comparatively benign" in the sense of "at least it acknowledges that people need somewhere to live") to outright supremacy rhetoric that entirely dehumanises Palestinians and is basically indifferent as to whether they just go or die. All of it, however, is deeply routed in a mindset of tribalism, though.
There are many more aspects to the question of settlements, of course, such as the fact that, especially in the areas around Jerusalem, a lot of people simply live in settlements for the economic advantages, such as the fact that the entire political project of Netanyahu has been to make a two-state solution impossible, and settlements are the primary weapon, by which this war is waged, etc. I'm not going to write an entire essay on MN.
... but your question was "how do people morally justify it?", and this is, broadly, what I have heard from the horse's mouth and read over the years.