You are not huring your child by saying “no”. I know it may be hard to do, and I know we all don’t want to put up with the tears and tantrums, but sometimes, you have to say “no”. Your child will love you for it in the future. There are some things that children are just not supposed to do and/or have and that’s just the way life is. Your parents said “no” to you, their parents said “no” to them.
They may hate you for it, for a few hours, a day, whatever. Stick to your guns. You’re the parent, and that means that you’re not always the good guy. It may not sound like it, but this is going to make your life easier in the long run.
Life is not fair.