The surface goal of the space program is to put someone in space, the moon, Mars, etc.
The real goal has nothing to do with this.
Private industry does not have the resources to create new science and inventions.
Without a space program we would not have computers, the internet, velcro, high efficiency thermal insulating fabrics, silicone caulk, microwave safe ceramics, nylon electrical ties, and hundreds if noth thousands of other articles used in our daily life.
It was even the Army who invented antibiotics.
You're kidding, Mister Central Government, right?
Private industry has always led the way with meaningful inventions, because it has the greatest financial motives to do so. Government does so only inefficiently and erratically, and at far, far, greater costs.
Private industry would have a lot more resources if our bloated government were downsized and taxes followed suit. It's a malicious joke to tax people and then say "haha, you can't do ____ as well as our rich, well-funded government. Guess you need government after all!"
The notion that the space program gave us computers is so historically ignorant I won't comment.
Likewise, while there are many spin-off inventions from the space program, think how many more inventions we would be enjoying if the engineering and technical resources spent by government on its space programs were in private hands, meeting real wants and needs expressed by the free markets and the citizenry? We would inherently be better off with the more direct application of scientific resources to our own wants and needs, rather than getting the crumbs from the table of Big Government.