Your children come from you and your partner and while they will have their own personalities and quirks, they also have many qualities they received biologically from you and your partner. Such things include temperament and shyness or extroversion. In addition to this, their personality and social behaviors will be deeply influenced by the way you and your partner respond to each other and to them. I have posted about the importance of appropriate parental interaction and how this interaction impacts children emotionally. Therefore I won't focus too much about that in this post. However, I do want to point out how you can learn about yourself through your children's responses to you.
First and foremost, we have to start on the same page that children mirror their parents. They mirror their parent's verbal/non-verbal interaction, emotional responses to each other, and social interaction with others. Children are always watching, listening, and learning, even when it doesn't seem like they are. To be fair, there are certain behaviors that children engage in because they are kids (ie. tantrums, whining, etc). The behaviors I'm referring to are patterns that have been established due to their re-occurrence. For example, a 2 year old tantrumming is ok, but a 10 year old tantrumming is not.
So what can you learn about yourself? For one thing, if your child has an irritating habit (leaving things around, yelling, complaining, etc) then the best way to address it is by looking at yourself first. Ask yourself how you might be contributing to this habit. Do you yell at your child and then pick up the mess for him/her? Do you often complain about your spouse, how you look, your neighbors. etc? Perhaps these are clues about your behaviors. If your child tends to engage in irritating behaviors that mirror your partner, how do you respond? Most likely the way you respond to your spouse will be similar to the way you respond to your child. So if you are aware and can find a positive way to respond to your child, that solution could also work with your partner.
Lastly, parenting to meet your child's needs is about keeping in perspective what your child needs to grow physically, emotionally, and socially at that given time. For example, when your child is being punished, do you often let your guilt sway you into getting your child a lesser or no consequence? If so, then you are parenting to meet your needs. Your need to feel loved by your child or to be accepted has gotten in the way of your child's need to learn that choices have consequences, and that he/she must learn to accept those consequences.
It takes a lot of strength to look at yourself in the mirror and admit any faults. But doing so will allow you to be a more present and aware parent, and intentionally model behaviors for your children. When people say that parenting is the hardest job you'll do, they are correct.