Why were the US and the Soviet Union unable to agree on the number of warheads and strategic bombers and the disagreement about the way in which...

One of the central tools used for analyzing this kind of conflict is game theory. The central premise of game theory is that decision-making agents (in this case, national governments) are in competition and act in their own self-interest. This isn't always a good approximation of human behavior, but during the Cold War it seemed to fit the conflict between the US and USSR quite well.

Both the US and the USSR wanted their ideology and way of life to spread throughout the world, but more importantly they didn't want their people to be killed in nuclear war. So at first thought, one might think that both nations should agree to disarm nuclear weapons and thereby avoid the worst outcome for everyone.

But many leaders of both nations felt that getting rid of their own nuclear weapons would be bad, because it would undermine their secondary goal of spreading their way of life. Essentially, if one nation had vastly more nuclear weapons than the other, it would have the power to act with impunity in achieving its global ambitions. But since both nations were trying to have more nuclear weapons than the other, the result was that both nations had a huge and roughly equal number of nuclear weapons, making them strictly worse off than if they'd just somehow agreed to produce no nukes at all. This is what in game theory is called a Prisoner's Dilemma; each agent acting in their own self-interest results in an outcome that is worse for everyone than if all agents had somehow agreed to cooperate.

You can also extend this theory to the question of deception; if one nation  can make the other nation think they have far fewer nukes than they actually do, then they could establish a strategic advantage while pretending to disarm together. Then they could suddenly pull open the curtain and reveal their total nuclear dominance, forcing the other power to capitulate. So both nations now have an incentive not only to build more nuclear weapons, but to do so in secret. But conversely, they also have an incentive to conduct inspections and establish punishments for creating nuclear weapons in secret---because they want to do it, but they don't want the other side to do it.

As a result, it was in each nation's self-interest to push for disarmament and inspections, but also in each nation's self-interest to find a way to structure the disarmament and inspections so that they could get away with producing nukes in secret. This tension is why there was such fierce disagreement over the precise terms of the treaty and how they would be enforced. The US wanted to establish inspections that would be hard for the USSR to escape, while the USSR wanted to establish inspections that it could escape easily; and vice-versa.