would you check my paragraph for me ?

The final argument is that parents do not seem to be the best teachers.

Some of parents don't understand their children, because they don't have enough time to be close to children.

I do not think it's a big problem.

For example my family is dual-income family.

"Dual-income" isn't used very often in American English. It would be more common to say "Both of my parents work", but this way is understandable too.

So when I was a young, I couldn't spend many much time with my parents, but I tried to follow and learn our my parent's behaviors and I think it made me improve my personality.

The final argument is parents seem not to be the best teachers.

Consider 'Finally,' or 'Lastly,' instead of 'The final argument is'

Some of parents don't understand their children, because they don't have enough time to be close to them.

Unnecessary repetition of 'children' sounds strange.

I don't think it's a big problem.

So if parents show them their good behaviors and good ideas it will not be a big deal.

It will be not big deal.

Attached to previous sentence.

For example my family is a dual-income family.

I agree with FrozenSkies. I've never heard 'dual-income' used in British English either.

So when I was a young, I couldn't spend much time with my parents, but I tried to follow and learn my parent's behaviors, and I think it made (or 'helped') me improve my personality.