According to psychological reasoning, which can be equated to simple
mathematic problem solving, there should be proof, according to any
discipline of science or observation to believe in anything. Then what
proves that assertions of a certain religion are flawlessly correct?
This are so many wrong assumptions I do not know to start. First of all, there is no such thing as "flawless" proof in science. With a very high amount of observations we have distilled certain statements like energy, momentum or angular momentum conservation which we believe to be correct with an extremely high degree of certainty. That does not mean that they cannot be invalidated with further observations (in fact during extremely short durations energy conservation may be violated), therefore there are not flawless.
Mathematics is only flawless because it specified rules in advance (axioms) to be true. These axioms could be extended (like non-euclidean geometry) to get new, unexpecting results. And in all cases human error could always mitigate presented results, so "flawless" is a insurmountable obstacle.
Second, there is no need for a "proof" for every thing people believe. I do believe that I am "existing" (whatever that means) without proof. So do I believe that I like vanilla ice. The things which should be regarded as important are things where several observers could have different opinions and there should be only one possible result for all observers. Another problem to find a proof is the Münchhausen trilemma; you must always leave options open which could invalidate your proof.
Third, religions do not always claim flawless correctness. While the monotheistic religions have a knack to claim such a thing, many religions are much more open about the interpretation and validity of their belief system.
Also, if a person is bound by a religion, probably due to his or her
birth, why should he or she believe in the teachings of a discipline
that's not proved? Isn't it misleading people?
We as humans have the need to get an identity. Who are we ? What is our
purpose in life ? Our surrounding and upbringing imparts a deep
psychological impact into what we think who we are. People will
necessarily try to teach their children what they believe is right and
good. Given that parents are also very protective of their children by
nature, it is a hopeless attempt to prevent that.
As everyone can see, many people stop believing their teachings,
especially if they find out that their parents do not really believe or
believe only that what it convienient to them.
So what ultimately forces me, or any other person, to be binded by a
religion and follow it? Of course, I can unsubscribe to a religion,
but that cannot happen in all cases, which creates a human society of
nearly blind followers.
Nothing except peer pressure can force someone to be binded by religion.
The purpose of religion is in my opinion not really related to flawlessly
explain the world, but building up a self-image, find a social structure for
participating and find a way to cope with the most pressing human
problems (purpose of life, love, sorrow, death, loneliness).
This also explains why attempts by naturalists of converting people
are not so successful as expected; if they could offer a convincing
alternative to live a happy and fruitful life, I suspect people will
flock to join the given alternative.
Monotheistic religions are desired because they offer a easy solution
(Follow this rules and you are good, deny them and you are bad), they
remove much sources of conflict (This is true, so you do not need doubt
and quarreling. This guarantees salvation, so you do not need to
think over if your actions are in the best interest of yourself and
other people), they are easy to understand and follow (allowing as much
people as possible to join the religion) and they give a powerful feedback
because everyone will tell everyone how happy he is (even if this is not
ADDITION: The question you now ask is if scientific and religious assertions
are different in quality. Scientists and philosophers always struggled to come
up with a clear-cut, crisp definition what a "scientific assertion" would be, but if
you allow to be vague, a scientific assertion in its ideal case should be
- self-consistent (no logical flaws)
- it should explain facts and with this
explanation it is possible to predict currently unknown facts or shed light
in unexplained matter
- it does not involve anything which is not already known, subjective or superfluous
- and its predictions should be checkable to evaluate its truthfulness
Just for info: Atoms were seriously considered as incorrect assumption by prominent scientists like Ostwald and Mach during the beginning of the 20th century.
Some religious assertions are illogical: Genesis claims first that animals came before humans and one page after that claims its exact contradiction. Take the four evangelists versions of Jesus resurrection side by side and try to get a consistent picture.
Some are outright bizarre: The all-knowing omnipotent God needs to move after Moses to kill him in an inn ?! (Exodus 4:24).
Some religious assertions are (almost) impossible to verify: Is there a God (if you describe it more from a pantheistic viewpoint) ? Is there a Hell ?
So many, many religious assertions cannot be considered scientific or even rational. Given your previous question I assume that you really want to ask: Why not replacing the religious assertions with scientific ones ?
Uh, well, because it does not work ? The current scientific viewpoint has a severe problem to judge behavior. They are not able to say: This is good and this is bad. You could try to ask the anthropologists for general human laws to form a base of understanding to work from. And they will come back and tell you that they asked the (very aggressive tribe) and the (very peaceful tribe) and it is absolutely hopeless to find a least common denominator. Worse, every attempt to write down a general rulebook of behavior will seriously piss off some cultures and the author will be called supremacist/racist.
And it also ignores reality. The people who call themselves XYZs ignore often inconvienient assertions about their religion XYZ. For your example: Alevi women are not forced to hide their face even if Alevism is considered a part of Islam, so your allegation is not always true. The Western World where most people still call themselves Christian do not stone homosexuals even when the Old Testament strictly demands it. The jewish life is a never ending battle of breaking extremely inconvienient and intricate historical laws in the present by finding loopholes, unintended exclusions and creative interpretations.
And people who call themselves rationalists can be exactly as illogical and emotional when conclusions does not fit their worldview. Penn & Teller have served the public a steaming pile of their own bullshit when they questioned global warming and recycling because it offends their liberatarian worldview.
So while people would like to have scientific guidelines, I do not think that it is possible to get ones for the mentioned reasons above.