I've read that using genocide as it relates to American Indians contentious among historians. Is it and why?

To start off with there are definitional arguments. Not everyone agrees with what genocide means. One can get around that by using specific definitions like provided in the UN Convention on the Prevention and Punishment of Genocide.

Article II: In the present Convention, genocide means any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:

(a) Killing members of the group;

(b) Causing serious bodily or mental harm to members of the group;

(c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;

(d) Imposing measures intended to prevent births within the group;

(e) Forcibly transferring children of the group to another group.

That at least gives us a point to start a discussion. But it also immediately poses several immediate challenges. The genocide of Native Americans (if such a thing exists) was carried out over many generations by a whole array of groups formal and informal.

Intent is a significant part of the UN definition. Simply killing people by itself isn't genocide, one must be killing them with the intent to destroy them as a group.

It's pretty easy to say that the Pequot War of 1634-1638 was a war of genocide. It was (successfully) engaged in order to eliminate the Pequot as a distinct group. By the end of the war most Pequot were dead and the remanded had their identity erased and were forcibly enrolled in the allied tribes of the English. That is one of dozens to hundreds of smaller instances where most everyone would agree a group of Europeans engaged in genocide.

It's less easy to say that 17th century English policy on the whole had a genocidal intent. Mostly they were happy to engage in peaceful trade with native peoples. An absolute ton of natives still died from English causes, disease in particular, that the English never intended. But under the UN definition, such deaths couldn't be counted as genocide. The death of Tsquanto's people, the Patuxets, before the arrival of the English is an example of deaths that wouldn't count as genocide by this definition.

There's also no doubt that there were always people among the Europeans who always intended the destruction of all natives. So we can also quickly go into the weeds as to how many people have to have intent before claims of genocide can be issued. The elders in Plymouth were pretty much in agreement over the Pequot, as were the soldiers and most of the populous. But other incidents were done with far less agreement or popular support.

We're only a sentence into one possible definition and I've already identified several potential points of argument. And not everyone uses the same definition as the UN; they may remove the intent element for example, which would make it easier to claim genocide.

It's pretty easy to make claims of genocide when you look at certain specific instances. It becomes a lot harder when considering the entirety of the Americas across the 15th through 20th centuries and policies of dozens of different countries and governments. European genocide of Native Americans is an incredibly broad claim, which requires a broad definition of genocide. As such it'll be endlessly argued over. Specific claims such as the English in Plymouth committed genocide against the Pequot, are far easier to make and defend. As such that tends to be a much more broadly supported among historians.