Question

Проверьте пожалуйста мое эссе. Исправьте ошибки
Many parents allow their children to keep the animals in the house. For children's entertainment and fun game.
I would like to express my opinion on this problem. I think it is a good idea. Firstly care about animals learns a child responsibility. Secondly friendship with the pet since childhood learns children to love and respect the animals.
On the other hand, many parents believe that young children can not take good care of their pets and pay them enough attention.
I do not agree with this opinion because for children is essential to learn to be responsibility for another's life.
In conclusion, we can say that looking ater pets from a young age is a good idea. Pets are very good friends for children.

Answer 1

keep animals without "the". What is that " 's " for in the second sentence

"Taking care of animals" instead of  "Care about animals"
"teaches children to be more responsible " instead of "learns a child responsibility"

I corrected the text and it looks like that.
. 
Many parents allow their children to keep animals in their  house. For children this is an entertaining and  funny game.

I would like to express my opinion on this problem. I think it is a good idea. Firstly, caring about animals teaches a child to be responsible. Secondly, friendship with pet which exists from childhood teaches children to love and respect  animals.
On the other hand, a lot of parents believe that young children cannot take good care of their pets and pay them enough attention.
I do not agree with this opinion because it is essential for children to learn to be responsible for another's life.
In conclusion, I think that looking ater pets from an early age is a good idea. Pets are very good friends of children.

Seems that you confuse learn and teach

learn - учиться
teach - научить