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Paying for pre-K can qualify for a tax break, but unfortunately paying for private kindergarten or a private elementary school never does. If you qualify, you get your tax break not as a deduction, but rather as a child-care tax credit.
Putting your child in pre-K to get a head start on his/her education doesn't entitle you to the credit. You can only claim the credit if you need your child to be in the pre-K program so that you can work or look for work. If you're married and filing a joint return, you and your spouse must both be working or job-hunting to claim the child-care credit.
Hope this helps! Please feel free to comment with any additional questions I would be happy to help. Best regards and thank you for using TurboTax!