From Wiki: Overseas Citizenship of India
Jawed Naqvi is wrong when he says India denied Pakistani and Bangladeshi citizens the option of acquring dual Indian citizenship. India does not offer dual citizenship to any person instead she has created a provision for a new form of Indian nationality know as Overseas Citizenship of India (OCI). An OCI is a person who is treated like an Indian Citizen but is not really an Indian Citizen. Jawed's primary complaint is that the OCI provision excludes two countries specifically and is a show of pettiness by the Government of India (GoI).There now exists a provision for a new form of Indian nationality, the holders of which are to be known as Overseas Citizens of India. The Constitution of India does not permit dual citizenship or dual nationality, except for minors where the second nationality was involuntarily acquired. Indian authorities have interpreted the law to mean a person can't have a second country's passport simultaneously with an Indian one — even in the case of a child who is claimed by another country as a citizen of that country, and who may be required by the laws of the other country to use one of its passports for foreign travel (e.g., a child born in the United States to Indian parents) — and the Indian courts have given the executive branch wide discretion over this matter. Therefore, Overseas Citizenship of India is not a full citizenship of India and thus, does not amount to dual citizenship or dual nationality.
The Central Government may, on application, register any person as an Overseas Citizen of India if that Person is of Indian Origin and is from a country which allows dual citizenship in some form or the other. Broadly speaking, a "Person of Indian Origin" is a citizen of another country who:
was a citizen of India on 26 January 1950 or at any time thereafter; or
was eligible to become a citizen of India on 26 January 1950; or
belonged to a territory that became part of India after the 15th day of August, 1947; or
is the child or grandchild of a person described above; and
has never been a citizen of Pakistan or Bangladesh.
The explanation for this exclusion is very simple and quite obvious. Any person who was an Indian citizen or is the child or grandchild of an Indian citizen (i.e. works for 3 generations of Indian heritage) is eligible to become an OCI. Even after 62 years of Independence, almost all citizens of these 2 countries would be eligible for an OCI without the country exclusion clause and the 26 January 1950 date clause. Pakistan and Bangladesh were formed by breaking away from India. The people of these countries fought a blood battle to be recognized as a separate country from India and a separate people who were not Indian. They claimed of becoming victims to hegemony and unfair treatment by the majority of Indian citizens. If India offered Pakistani and Bangladeshi citizens an OCI status, then they would defacto become Indian citizens without the right to vote (an OCI does not have the right to vote). They would thus complain of their second class citizenship status and claim vindication of their worst fears of unfair treatment by the majority of Indian citizens. In this case there is no good outcome for India other than to let the country exclusion clause and the 26 January 1950 date clause work till such a time when the people of these 2 countries feel secure in their unique identity and shed their fears of unfair treatment by the majority of Indian citizens.
These clauses represent a sincere attempt by GoI to preserve the honor and dignity of the Pakistani and Bangladeshi citizens and tries to protect their unique identity which was separate from their Indian heritage.