It is generally thought that if women decide having a baby
This should be “if women decide to have a baby.”
Fathers are ignored about raising a child.
This is… just not well said, at all. First, it should be “fathers are ignored when raising a child.” But I know that this is not the message you’re trying to convey. What you’re actually saying is that they don’t have as much responsibility as mothers do. If you want to keep a similar sentence, then, “Fathers are ignored in the matter of raising children.” But I’d rephrase it completely to say something like, “Society places less responsibility on fathers as far as child-rearing is concerned.”
First of all, father, who play a vital role in a family
It should be either “fathers, who play a vital role…” or “father, who plays a vital role…” In other words, you’re either using the plural of father (so there’s no need for s at the end of the verb) or the singular father (in which case, the third-person singular has to end in -s, so he plays a vital role).
considered to be a breadwinner in many countries
is considered to be a breadwinner in many countries
and most people believe that fatherhood is extremely important , as much as motherhood.
Added a comma there to make the meaning clearer.
Children need to their father while they are growing up.
“To” is incorrect. It’s just “children need their father.” Also, growing up is the process of becoming an adult. Just growing is the process of becoming bigger.
In other words, children who grow up without their father feel themselves like uncomplete.
“In other words, children who grow up without their father feel incomplete.”
First, you don’t “feel yourself.” You just “feel” a certain way. Those are the dangers of literal translation 
Also, the correct form is “incomplete.” It means “missing something.” You may have been thinking about “uncompleted,” which means “something slated for completion but not completed.” As you can see, “incomplete” is the adjective you were looking for here.
As a result, they can be very upset and hopeless individuals in their future life.
Again, poor phrasing. “Upset” and “hopeless” are not adjectives I’d use together. “Upset” is what you feel in a moment; “hopeless” is a more general feeling. I’d say more like, “they can be very unhappy and hopeless individuals in the future.” As for the second part, “in their future life,” it’s not incorrect, but it’s also not something a fluent English speaker would say. I’d just go with “in the future.”
can encounter psychological problems in their adolescence , according to a recent survey by Harvard University
Added a comma because that information is non-essential, and you’d pause for breath there if you were reading out loud. Also added “a,” since it’s a single survey you’re referring to, and it was done by Harvard University – it’s not done of Harvard University. It’s just a shortened passive form.
Therefore, fatherhood should be considered to be essential for children’s psychological development.
Remove “to be.” It’s not necessarily incorrect, but it sounds much better when you say just “considered essential.”
When comes to motherhood
When what comes to motherhood? The correct form is “when it comes to motherhood.” You’re answering the question of “what” that I asked (no matter how dumb that question sounded when you first read it) by replying, “it.” Alternatively, you can just remember that “when it comes to” is a phrase that is always used in this form.
motherhood does not give the right to mothers
You’re not referring to some vague right – you’re talking about a concrete right, so it’s “the,” not “a.”
the right to mothers about caring for alone their child.
Everything is wrong here. First, the word placement. It should say, “caring alone for their child.” But a right cannot be given “about.” It’s always given to someone, to do something. That becomes “… the right to mothers to care alone for their child.” Using “to” also changes the verb’s tense to infinitive, as you probably noticed.
But there’s also the matter of meaning. In fact, yes, motherhood does give mothers the right to care for their child by themselves, as evidenced by a number of single mothers, no matter what their circumstances are. What you seem to be trying to say is that they shouldn’t be forced to care for their children alone. In that case, you can say something like, “motherhood does not force mothers to care for their child alone.” Remember, you can get everything correct in terms of grammar, punctuation, and vocabulary, but still not convey your meaning properly. Unfortunately, that’s a common problem for many learners.
There is no doubt that fathers should take care of their baby, too.
“Baby” should be plural, ie “babies.” Otherwise it sounds like there is more than one father taking care of a single baby. What you want to say is that each father should take care of his own baby, which means there are multiple babies.
Children’s requirements ought to be afforded well by their parents , and the best way for that is raising the children together.
You’re connecting two independent sentences here, so there should be a comma. Also, children don’t really have “requirements” – that’s a word we mostly use for inanimate objects, like hardware requirements to run a game. Generally speaking, humans have “needs.”
Also, children should be educated at the best school because children’s education should be the most crucial topic for their parents.
First, it should be “schools.” Otherwise you’re implying there is only one school in the world that is the best, and all children should be educated there. We know that’s impossible, so we use the phrase “the best schools” to refer to the schools that are better, relatively speaking, than the others in the vicinity.
Also, it’s either “a crucial topic” or “the most important topic.” The word “crucial” is already superlative, so adding “most” doesn’t work there (it’s like saying, “the most best food.”) But I appreciate that you use “crucial” correctly, so you can stick with it.
To put it another way, father, who believe that importance of family, can provide a nice life standard to his baby while contributing to his home.
It should be “a father.” It’s a countable noun. In that case, it should be “believes” – see above. Additionally, you can’t believe “that importance.” You can either “believe that family is important” or “believe in the importance of family.” Stick with the second one if you want to keep the sentence close to the original.
The good illustration of this, the child can be sent to a school, which is the best but has an expensive fee, when the father took responsibility.
“A good illustration…” because it’s not the only illustration. You’re just showing an example and there are many more out there. Let me correct the whole sentence: “a good illustration of this is that the child can be sent to the best school that is also expensive when the father takes responsibility.” It’s slightly shorter, sounds better overall, and you’re staying consistent in terms of tense. If a child “can be sent” somewhere, then the father “takes” responsibility. You have to keep the same tense everywhere.
despite some people believe
It’s “despite some people believing.” You have to add -ing to the verb when you’re using “despite.”
women can take care of their baby
Women can take care of their babies. Same as above – it’s not one baby and several women, it’s many babies and their mothers. Both should be plural.
I think that the baby should be raise
“Should be raised.” Passive form uses past participle.
