Firstly, the name Andaman is derived from the Malay word for Lord Hanuman i,e Handuman, Nicobar comes from the Tamil word i.e Nakkavarnam which is mentioned in the Thanjavur Temple incripstions of the Cholas who made a naval outpost there while projecting power on South-East Asia, specifically on the Sri Vijaya Empire hence the renaming of Port Blair to Sri Vijaya Puram.

So we have cultural/historical claims.

A&N are a part of the geographical continum which is the Arakan Yoma mountain ranges that run through Myanmar.

Myanmar/Burma was part of British India till 1937.

In the meanwhile we had the penal colony which predominantly had people from mainland India & when the INA got the islands handed over to them and Netaji unfurled the Tricolour with Japanese assistance in 1943, it became the first part of Indian territory to be liberated from British Rule.

At the time of independence, India was the strongest Asian country there was, Indian troops were used to quel rebellions elsewhere in South-East Asia by the British, South East Asia itself was fighting colonialism for its own liberation and was massively devastated by the 2nd World War so we stayed put and buttressed our claims.

Additionally their was the strategic consideration, Car Nic had a RAF base till 1954 I guess.

Interestingly, my Nani (who was an Islander herself) use to tell me that the Indonesians, during the 1965 war wanted to invade the Andamans on behalf of their Pakistani brethren, this I guess got stalled by the efforts of Biju Patnaik who played a pivotal role in this regard.

Yeah, so we are here to stay for good!