I read that if I give a gift of $10,000 to my daughter that I can't take a tax deduction? If this is true why is there a rule of gift giving? I am confused.

That's correct, there is no deduction for giving a gift to an individual. In fact, you can wind up paying tax on the amount that you gave away! This law was created to prevent wealthy taxpayers from giving away their money and property in order to avoid the Estate Tax.

Your daughter doesn't  have to pay tax on any amount that you give her. It's tax-free. But the donor may have to pay tax on extremely large gifts.  You won’t owe the tax until you’ve given away more than $5 million in cash or other assets during your lifetime. 

Gift tax returns would be required for someone who gave gifts of more than $14,000 in 2017. Otherwise, you don't need to file a return,or worry about paying gift tax.

See this link to an explanation of how Gift Tax works.