Okay, it's not fake, as in not real, but it's kind of a weak country, as far as history and logic. And please keep in mind I say this all as a Bengali with family from and in Bangladesh.
Brief context: What's now Pakistan and Bangladesh were both contained within what was historically India for as long as anyone can remember. Then the British came. Occupation and colonization were followed by Indian resistance, and then a departure of the British.
As a departing gift, in 1947, the British helped divide India into "Hindu" India and "Muslim" Pakistan.
As you can see, the newly created "Pakistan" was split into two parts. West Pakistan on one side of India, and East Pakistan on the other side of India. What could go wrong?
The new state of Pakistan, made up of two noncontiguous states, separated by India, in which two separate languages were spoken, and two separate and distinct cultures prevailed, would not survive for long. In 1971, West and East Pakistan had a civil war, in which India played a major role, helping East Pakistan gain its independence from West Pakistan, and thereby creating yet another new country: Bangladesh.
Here's the part that bugs me: Bangladesh, which came into being in 1971, is arbitrarily separated from West Bengal, as state in India that it borders. Calcutta, the capital of West Bengal, was historically the capital of Bengali culture, the cultural center of Bengali literature and science, etc. The region of the Bengal was defined by its language, Bengali.
Partition created a completely arbitrary line in the middle of the Bengal. One of the greatest mass migrations in human history accompanied partition, with Hindus fleeing into India, and Muslims fleeing into "West Pakistan." But nearly all of these people spoke Bengali. The closest parallels I can think of are the partition of Germany after WWII, and the partition of Korea after the Korean War. Both of those partitions clearly felt artificial, and against the grain of history, and the pull of a shared language and culture. The Wall fell in Germany. The DMZ will surely one day be cleared in the Korean peninsula. One wonders if the border between Bangladesh and West Bengal can be maintained. It actually would make more sense for West Bengal and Bangladesh to merge into one separate country than for Bangladesh to be maintained as a Muslim half of the region of Bengal, the remnant of the imagined country of Greater Muslim Pakistan.
What was the purpose of creating Pakistan? Hasn't the creation of Pakistan done more harm than good? Yes, Pakistan was created to allow Muslims to have their own state, but was there really a need for that? India has one of the largest Muslim populations of any country in the world (160 million). Yes, there is Hindu-Muslim strife, but India is a country bursting with various languages and religions. That's how it is now, and how it always has been. Quick, what's the first image you have when you think of India? The Taj Mahal, right?
That's a Muslim building, built by the Mughals: Muslim rulers of India from the sixteenth to the eighteenth centuries.
Anyway, I know there are all sorts of arguments to be made in response to this. But my point is this: the line separating Bangladesh from West Bengal is the same type of line that we tried to draw between East and West Germany, the same type of line that currently separates North and South Korea. A border like that is untenable, in the long run.