I have found it very common among Hindu's a reluctance to say they are Hindu when asked about their faith.
Reasons are many .
They have not resolved the questions about faith in their own mind.
They are still struggling with the definition of what is a Hindu.
They find it as an easy and true answer that they were born Hindu.
They are not sure what are they saying by declaring they are Hindu.Are they less human or more because of it.
It is easy for them to declare that belong to a sect or are followers of such and such Guru.
Some times they are reluctant to announce their faith if they have failed to fulfill the image they may have in their mind of the Hindu.
They do not find it necessary to do so.
So what is Hindu any way .
Definitions vary from some exotic faith to just inhabitants of a geographical area.
With the second definition people who live in the region from Afghanistan to Burma will fall into this category.I only accept this definition half heatedly.
I accept the more liberal definition which is Hindu is one who is trying to understand his relationship with the universe(Some may call it god).He thinks and feels that everybody has right to make their individual journey in this search.
He has reverence for all the sages ,prophets ,incarnations.
She/he may have a personal deity( or belief system) she believes in but she does not think that it is exclusive and respect all deities.Believes all the faiths pray to same god .In case of agnostic and atheist he believes that they are looking for answers to the questions about god and have not resolved them in a way many religious people have done it .He does not find any conflict with him.
In realty he is what Walt Whitman said about the man fits him perfectly .He the poet of America got the true sense of man and American and Hindu without saying so.
Now let us see why Americans have hard time declaring they are christian.
OH MY REASONS ARE THE SAME AS HINDU/INDIAN HAS HARD TIME DECLARING HE IS HINDU.In America Most people think that everybody is christian so declaration that one is christian is irrelevant.In India by the given name you would know if one was born Hindu,Muslim,christian,Sikh.At the same time because reverence taught one accepts it at face value.
Other than some foreign influenced christian missionaries and Muslim preachers and as reaction to them there is little effort today to convert people to join one or other faith.There are opportunist who want to take advantage of polygamy marriage laws for Muslims in India(British legacy of 1935 Government of India Act).Sadly it continues and some make a big scene by declaring they are Muslim and having plural marriages.These are shams and remain targets of public ridicule.
IT IS QUITE INTERESTING THAT INDIA IS ABLE TO GO FROM AGRARIAN ILLITERATE SOCIETY TO ONE RAISING METAPHYSICAL QUESTIONS IN SHORT PERIOD.May be the reason is that though illiterate, society has discussed existential and relational questions with and about god for centuries and they do not find it hard to reconcile it as well as any learned man of the west or east.