Americans were quite worried in 1996 about the fact that Ukraine was the world's third largest nuclear power and it was right next to Russia. The American government decided that they would rather deal with one major nuclear nation than with two major nuclear nations. And they were also afraid of a future nuclear war between Ukraine and Russia.
Condoleeza Rice was the main person who was sent by Bush I to "encourage" Ukrainians to give up the nukes in exchange for security promises. (Her PhD thesis was in Soviet military history.) If United States really will defend Ukraine in the event of invasion, then it was probably a good deal for Ukraine.
Ukraine was the closest to the West, so it was the most armed area of the Soviet Union. At the time of the break-up of the Soviet Union, Ukraine actually had more tanks than Russia. And it still has a significant defense advantage compared with other nations its size.
Ukraine was also a major part of the Soviet defense industry. Ukraine still makes most of the engines for Russian military helicopters and missiles and provides many jet engines. The largest missile factory in the world is located in Dnipropetrovsk, Ukraine. It can make lots of missiles really fast.
Another interesting comparison is that Georgia had about 6 jet planes and 6 military helicopters. Ukraine has at least 600 fighter jets and I am not even sure how many military helicopters, along with one of the most advanced air defense systems in the world. (Ukrainian-designed Kolchugas can shoot down even stealth airplanes.) Any conflict between Ukraine and Russia would result in huge losses on both sides, both in human casualties and in expenditures on war.
That's another reason why it would be insane for Russia to invade Ukraine. They could loose the war, even without Americans entering the fight. In any case, their military would at least be badly damaged. What they are more likely to do is try to destabilize the situation in Ukraine from the inside, by supporting and financing various anti-Ukrainian groups inside Ukraine.
If you are Russia's neighbor, you better be strong (or have strong allies), because otherwise you are not going to be a nation for very long. That's the sad history of all of Russia's neighbors.