Question: I have a doubt in SVM for binary classification what is the problem if the hyperplane actual one and not passing through the support vectors

I have a doubt in SVM for binary classification what is the problem if the hyperplane actual one and not passing through the support vectors doesn't maximizes the margin distance as while predicting the classes the original hyperplane is used to make the prediction so there should not be much difference even if the hyperplane is not margin maximizing as what matters is the data point towards the left or right of the hyperplane I am not able to understand why maximizing margin minimizes misclassification probability and what it means by sensitivity to small changes and overfitting tendency with small margin distance can you clarify possibly with an example please

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