Answer
First of all, heartfelt blessings and good wishes to you and your brothers and sisters for conducting regular satsanga. The glory of satsanga is truly wondrous -- its benefits accrue both to those who conduct it and to those who listen.
Now, turning to your question -- why do the Avataras of God incarnate specifically on the land of Bharata (India)? This question should truly be asked of God Himself, and the answer should be obtained from Him alone, because God is absolutely sovereign. We have no control over His will. His lilas are mysterious, and their mystery has never been fully revealed. Nevertheless, this topic can be discussed from a certain historical and geographical perspective.
The land of Bharata has been extraordinary in many respects. Such geography is not available anywhere else in the world. It is protected on three sides by oceans and secured on one side by the Himalayas. Entry is possible only from the northwest and the northeast. Such variety of climates is also perhaps found nowhere else. In other parts of the world, although human beings may already have been born, they remained in a primitive state for a long time. Civilization and culture did not arise there. It is said that the first human was born in Africa, yet even today that continent is considered relatively backward and primitive. One reason for this is its geography. Geography profoundly influences history.
The geography of Bharata was utterly unique. There was a vast network of rivers here, and most of the land was green and fertile. Wherever there is abundance of water, agriculture, animal husbandry, and permanent human settlement develop. Agriculture and animal husbandry bring prosperity, and when prosperity comes, human beings gain some freedom from the daily struggles of sustenance.
When the anxieties of food and security diminish, the human mind and heart get the opportunity to focus on higher purposes. This is precisely why so many systems of philosophy developed in India.
For this very reason, agriculture and pastoralism began on a wide scale in the land of Bharata from ancient times, and in due course, the Rishis, freed from the anxieties of sustenance, found the opportunity to engage in contemplation, reflection, and meditation upon Brahman, the Atman, and higher truths. This is why you will observe that the Vedas were composed in the Sapta-Sindhu region and on the banks of the Ganga. While the rest of the world, including Europe, was still living a hunter-gatherer life, the seeds of culture and civilization had not merely been sown on the land of Bharata -- their mighty trees were already in full bloom. Profound discourse was taking place on higher subjects such as Satya, Ahimsa, Brahmacharya, Asteya, morality and immorality, and there was extensive churning on the nature of God as well.
Cacti may sprout in a desert, but delicate and fragrant flowers bloom only on soil that is moist, fertile, and conducive. When God saw that the consciousness of the land of Bharata -- its collective psyche -- had become ready for the sowing of seeds of divinity, He manifested His Avataras here and began communion with humanity.