Cold War- Space Race

While learning about the space race I became increasingly interested and curious as to why it became such a big deal. There are obvious reasons, such as the fact we would be making huge technological advances. Despite the huge leap in progress, I want to know why the space race was amplified by the leaders in the Cold War.
It all starts with the fact that Russia and the US were in a power hungry fight to be considered the top country. Fight is not the best word for this because no country actually ever did anything. Russia and the US through this war basically just flexed their muscles at each other, but never threw a punch. Once the US created a atomic bomb, and kept that from Russia despite their alliance, jealousy started. Russia thought they had the right to know about this because of the alliance, however Stalin stayed calm and collected because his spies had been informing him. Once the US had finally tested and used this nuclear weapon, soon after Russia tested their first nuclear weapon. This was the first round of flexing their every growing muscles. Then the United States decided they would build up their muscles more by creating a hydrogen bomb. Once they tested the bomb, and it was hugely successful, the United States flexed their muscles once again almost gloating at Russia. Things cooled down slightly for a while, however when FDR made a comment about having better color TV than Russia, it was taken as another challenge. Russia then abruptly sent Sputnik, the first man made object sent into space, out into the sky shocking everyone. Sputnik never really did anything, just simply reminded the United States that they had gotten an object into space before us through sending a beep through our radios. This is where Russia flexed their muscle once more. This further provoked the United States to continue on with this childish fight.
The fact that this went on for so long shows us something very valuable. The two countries were in a power struggle and did not trust the other enough to simply back down and seem week. Both countries had the idea in their head that the other was going to attack them at any point in time, but this clearly was a huge misunderstanding. Russia wanted to build up their country, and the US just wanted to avoid all wars over seas. I find it ridiculous that countries will act like this just to intimidate the enemy or to become even more strong that they already are. This topic once again proves the point that in any type of war each country is only in it to do the best for themselves, and if it comes down to choosing between winning and losing at the cost of an ally, I would believe that they would only think of themselves. Honestly, war just makes people and their government one crazy mess.