I have an argumentative seven-year-old. He is bright; his logic astounds me, and even though I have degrees in how children's brains work (I'm a qualified teacher), the things that come out of his mouth never fail to leave me speechless.
He's not even what many experts would call strong-willed. While he may get frustrated and angered fairly easily (he is a child, after all), he usually deescalates and quickly goes back to his happy, little self. He's always been a pretty obedient little boy who, believe it or not, is a follower, even though he is not swayed by peer pressure. He has strong opinions and strong feelings, but they aren't overwhelming in a way that anyone would ever call him difficult, or even stubborn.
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He is, however, argumentative. He's smart, confident, and responds to nearly everything I say with, "Yes, but..."
As a mama who wants to gently and peacefully parent him (my husband and I have done that fairly well so far), I sometimes have a hard time entertaining certain arguments, especially as he's getting older and more knowledgable/logical. His arguments often leave me feeling defeated and him feeling guilty about upsetting me.
One of the first things experts will recommend is remembering that you simply don't have to be part of every argument! While your child may have a rebuttal for your mere breathing (or so it may seem!), just don't entertain it. Take a deep breath, hold it and excuse yourself. If you are in the middle of battling about why it's important to wear a coat, make your claim (it's cold; you need a coat), let your child know you are aware of their position (I understand you don't feel you need a coat, but I do, and it's my job to protect you), and leave the argument.
Sometimes in wanting our children's feelings to be heard and recognized, we forget that we are still the parents who know best, and sometimes because you said it really is enough of a reason.
Another thing that's important to remember is that your child really is not trying to attack you personally. It seems so weird and fresh sometimes to hear these really grown-up retorts out of my baby's mouth, and it sometimes hurts my feelings. But the thing to remember is that most often an argumentative child is not arguing to be hurtful, but because he or she strongly believes in what they are saying.
No, they are not always right, but the strength and courage it takes to maintain conviction in light of even possible consequence is one that when guided gently will serve them well as adults. Our children love us. It is because they are secure in our unconditional love for them that they even feel safe enough to argue. So, while it may seem personal, it most likely is not.
Because your child really does believe that their side of the argument is the right one, sometimes the only thing to do is allow natural consequences to show them they were not as right as they thought. These children often have strong senses of morality and integrity, and learn experientially. You telling them something that they literally feel in their gut is not right just won't get through to them sometimes. No, it's only when they realize, "Oh, yeah. It IS cold out here," that you might find less of an argument the next time you are bickering about coats.
On the other hand, sometimes as moms, we'll set a mandate on something and our children really will have a better idea/way to do it. Instead of using those opportunities to maintain a "mom is boss!" attitude, stop for a second and think about what would happen if you were to give in to their side of the argument?
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Imagine the security your child would feel in knowing that you recognize you too are only human and they are competent little ones who have amazing ideas as well. Often, their ideas won't pan out, and that's a great way again for naturally consequential connections to be made. But at the same time, you are telling your child that you recognize his ideas and respect them, and are even willing to entertain them because you value them and him. That's powerful, and shows them they don't always have to be so argumentative to get their point across - you're listening to them and respect their words.
With my son, I find that win-win opportunities really curb arguments before they even happen. He once told me that, "Cleaning is not my spiritual gift, Mama," when I told him to clean up his playroom.
I have come to learn that giving him some reasoning behind my requests make the request happen so much more compliantly. When I ask him to clean his room so I don't have to, I also mention that it will give us more time to play a game or go for a walk. That motivates him.
It takes some creativity on my part sometimes to come up with rationale other than, "Because I said so," but I find when I lead off with that, the push-back he gives is so much less. And that makes for a happier household and relationship for us both!