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.
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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