Recently a question was asked about the reasons why many Hindus are opposed to the Aryan Migration Theory (AMT)? The question was asked in a manner that does not fit with the requirements of this site. So I have worded the question in a manner that best suits this site. I feel the question is important and it is important to get a scholarly answer that explains the reasons for the opposition.
There is no spiritual principle that is behind the opposition to AMT by many Hindus. The reasons for the opposition is spelled out very lucidly in this site: http://talageri.blogspot.in/2018/04/what-is-value-of-new-genomic-evidence.html?m=1
Sri Srikant Talageri is the principal Indian scholar behind the Out of India Theory (OIT).
The main point is that genetic data can not tell us definitively about language migration. Moreover linguistic theories are in direct conflict with archeology. Linguistic theories say that there was definitely migration into India by Indo-Aryan speakers while archeologists like Kennedy are equally sure that there was no migration by people with different body types in the time frame of the AMT or AIT theory. Moreover textual data from the Rig Veda and archeological data from Mittanis in West Asia are in conflict with the linguistic data. At least this is what I understood.
I am giving more explanation to further clarify the situation. It is not the migration of Indo-European speakers that is the issue. The problem is the insistence of the linguists that the migration occured around 1500 BCE. This creates problems with the Rig Veda since 1500 BCE is also the timeline of the Rig Veda. This raises the question as to why Rig Veda does not have any memory of inward migration into India. Another problem is with respect to Saraswati river. Rig Veda talks of the Saraswati river flowing from the mountains to the ocean. The Saraswati river stopped flowing to the ocean around 1900 BCE. If the Rig Veda was composed by the Indo-Aryan speakers around 1500 BCE the why should the Rig Veda talk of that river flowing to the ocean. There are also other issues that complicate understanding of India's prehistory.
This article http://archaeologyonline.net/artifacts/genetics-aryan-debate gives a good summary of the Aryan invasion debate.
No central Asian genes have been found in Rakhighari skeleton. https://economictimes.indiatimes.com/news/politics-and-nation/harappan-site-of-rakhigarhi-dna-study-finds-no-central-asian-trace-junks-aryan-invasion-theory/articleshow/64565413.cms
Evidence for chariots found in Bronze age dig site. http://www.newindianexpress.com/nation/2018/jun/05/uttar-pradesh-asi-unearths-first-ever-physical-evidence-of-chariots-in-bronze-age-1824138.html