That was why I searched for another bank. And that other bank accepted my application and my documents (requirements). I concluded to myself that TIN is not required to open a bank account in certain banks in the Philippines.
In my own thinking, not all people have TIN particularly farmers, fishermans, carpenters, laborers, salesladies, housewives, students and those who are engaged in micro-businesses or small businesses. They contribute the biggest chunk of the population of the Philippines. That's why most banks don't require TIN for their applicants or new depositors. We know that banks are very hungry of acquiring new depositors whose cash become additional asset to banks. Banks will use those cash to earn money from lending (loan) it to borrowers with interest or by investing it to the stocks or investing it to diversified investment vehicles.
For those who want to open an account in a bank that requires TIN, you can get your TIN online for free by reading this article: "How to Get TIN (number) Online in the Philippines?".
What do you think of banks that require you to submit TIN?