Is a withdrawal a business expense?

It rather depends what the withdrawal was for. If it was for personal use - then no, but if it was for petty cash for example - then yes.

The above gets there, but a withdrawal is NOT an expense of any type. It is simply getting cash from an account...you/business has no more or less after the withdrawal than before. Just where that asset is changes.

The expense may occur when you spend the withdrawal on a tax deductible expense.