I think people are overlooking why the idea of 'discovery' pisses off Native people-because it's associated with the 'doctrine of discovery' used to claim that Indigenous people didn't have any pre-existing rights in lands found by European explorers, and that justified the European powers exerting authority over them.
Here's a brief summary: $1:
2. Within the framework of the Doctrine, Indigenous Peoples in the Americas were considered non-human
The presiding theory of the time was that Indigenous Peoples, because they were non-Christians, were not human and therefore the land was empty or terra nullius. When Christopher Columbus arrived in 1492, it is estimated that the Americas were actually occupied by 100 million Indigenous Peoples - which is about one fifth of the human race at that time - who had been living their traditional lives on the land since time immemorial. But, because they were not Christians the land was deemed terra nullius.
...
3. The UN’s perspective on the Impact of the Doctrine of Discovery (May, 2012)
“The Permanent Forum on Indigenous Issues concluded its eleventh session with the approval of a set of nine draft recommendations, highlighted by a text approved on the special theme, the ongoing impact of the Discovery Doctrine on indigenous peoples and the right redress. That fifteenth century Christian principle was denounced throughout the session as the “shameful” root of all the discrimination and marginalization indigenous peoples faced today.
The Permanent Forum noted that, while such doctrines of domination and “conquest”, including terra nullis and the Regalian doctrine, were promoted as authority for land acquisition, they also encouraged despicable assumptions: that indigenous peoples were “savages”, “barbarians”, “inferior and uncivilized,” among other constructs the colonizers used to subjugate, dominate and exploit the lands, territories and resources of native peoples.” [1]
And from the TRC...$1:
Other European rulers rejected the Pope’s ability to give away sovereignty over half
the world. But they did not necessarily reject the Doctrine of Discovery—they simply modified it. The English argued that a claim to ‘discovered lands’ was valid if the
‘discoverer’ was able to take possession of them. Harman Verelst, who promoted the
colonization in the eighteenth century of what is now the southern coast of the United
States, wrote that “this Right arising from the first discovery is the firrst and fundamental Right of all European Nations, as to their Claim of Lands in America.” This
Doctrine of Discovery was linked to a second idea: the lands being claimed were terra
nullius—no man’s land—and therefore open to claim. On the basis of this concept,
the British government claimed ownership of the entire Australian continent. (There,
the doctrine of terra nullius remained the law until it was successfully challenged in
court in 1992.) Under this doctrine, imperialists could argue that the presence of
Indigenous people did not void a claim of terra nullius, since the Indigenous people
simply occupied, rather than owned, the land. True ownership, they claimed, could
come only with European-style agriculture.
There's a reason why the Truth and Reconciliation Commission has called on us to abandon the idea of 'terra nullius'. And if you don't trust the UN's position on it, here's the position of the Church itself...
$1:
Regarding the question of the doctrine of discovery and the role of the Papal Bull
Inter Coetera, the Holy See notes that Inter Coetera, as a source of international
law … was first of all abrogated by the Treaty of Tordesilles in 1494, and that
Circumstances have changed so much that to attribute any juridical value
to such a document seems completely out of place.… In addition, it was also
abrogated by other Papal Bulls, for example, Sublimis Deus in 1537, which
states, “Indians and all other people who may later be discovered by Christians,
are by no means to be deprived of their liberty or the possession of their property
… should the contrary happen, it shall be null and have no effect.”
This view was expanded upon and reinforced in Immensa Pastorum of [Pope] Benedict XIV
of 20 December 1741 and a number of other Papal Encyclicals, statements and
decrees. If any doubt remains, it is abrogated by Canon 6 of the Code of Canon
Law of 1983 which abrogates in general all preceding penal and disciplinary
laws.… Therefore, for International Law and for the Catholic Church Law, the
Bull Inter Coetera is a historic remnant with no juridical, moral or doctrinal
value.… The fact that juridical systems may employ the “Doctrine of Discovery”
as a juridical precedent is now therefore a characteristic of the laws of those states and is independent of the fact that for the Church the document has had
no value for centuries. The refutation of this doctrine is therefore now under the
competence of national authorities, legislators, lawyers and legal historians.
TL/DR: The basis for European colonization of Canada, the U.S. and elsewhere was the Catholic Church's 'doctrine of discovery', based on the belief that non-Christian peoples were subhuman and had no actual rights to whatever lands they were living on. That doctrine was itself repealed by the Catholic Church centuries ago. Unfortunately, from the Indigenous point of view that same mentality still remains in ignoring their constitutional Treaty rights, and the assumption that they should shut up and assimilate. They never consented to that in the first place-from everything I've seen, historically and today, the vast majority of Native people have never objected to having the rest of us as neighbours, or even seeing themselves as our fellow citizens in many cases...but they're still seen as backward savages and their land rights not seen as worthy of considering.
That's the problem here-the attempt to forcibly erase their identities and ignore their land rights.