I pad 4 won't let me update browser why? Model A1458

Your iPad is now over a decade old, and lacks the hardware required to be updated past iOS 10.3.5. It simply doesn't have enough Ram. Safari is built into iOS. If iOS can't be updated, the browser in iOS can't be updated.

You're welcome. You have to admit the fact you're asking about a 10 year old device is pretty amazing. Technology evolves. It's time to invest in a newer, more modern iPad.