Loss function for Logistic Regression

If we are doing a binary classification using logistic regression, we often use the cross entropy function as our loss function. Question: However, if we are doing linear regression, we often use squared-error as our loss function. Are there any specific reasons for using the cross entropy function instead of using squared-error or the classification error in logistic regression? I read somewhere that, if we use squared-error for binary classification, the resulting loss function would be non-convex. Is this the only reason reason, or is there any other deeper reason which I am missing?