I have recently become very interested in the linguistics in the problem of the Indo-Aryan migration controversy. I understand in the early 19th century India was favored as the Proto-Indo-European homeland, but then after the development of comparative-historical linguistics that fell out of favour and the Southern Russian one was preferred. In fact it seems there are three major homelands. In addition to the Southern Russian one, Anatolia and Armenia both seem to be taken seriously and have academic currency.
However, I don't understand why the Indian homeland theory is excluded from all discourse and considered fringe. It seems the Indian homeland was initially the most favoured one. The flora and fauna of reconstructed PIE lexicon all seem to point to India (elephants, lion, etc.); syntactically, Sanskrit is the closest to PIE having retained all eight cases, three genders and three numbers, and the original PIE culture only is preserved by India. However, phonetically, PIE is very distant from a Vedic language, mainly because it sounds like a Centum language. So it seems syntactically it is near identical to Vedic Sanskrit, and phonetically it is very different from Vedic Sanskrit, yet still retains archaic forms, like aspirated plosive sounds, such as Bha, lost everywhere else.
However, is it still not possible PIE originated in India, the Centum branches left early and then PIE changed into Vedic Sanskrit at home? Considering that Balto-Slavic is a Satam language and it originated where PIE use to be spoken, cannot the same apply to India?
I do not mean to be antagonistic with this question. I just want to genuinely understand what are the linguistic evidences that preclude India from being a homeland of PIE. All I know so far according to linguistics it is impossible, but I don't know why it is impossible.