Why the topic of quantum entanglement is at the heart of the disparity between classical and quantum physics. Why entanglement is a primary feature of quantum mechanics not present in classical mechanics?
The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics because it is a primary feature of quantum mechanics that is not present in classical mechanics. Entanglement occurs when two quantum systems become correlated in such a way that the state of one system is dependent on the state of the other, even when they are separated by a large distance.

In classical mechanics, such correlations between objects are not possible because classical objects have definite properties, such as position and velocity, that can be determined independently of each other. However, in quantum mechanics, the properties of particles are described by wave functions, which can be in a state of superposition, meaning that the particle can exist in multiple states simultaneously. When two particles are entangled, their wave functions become entangled, resulting in a correlation between their states that cannot be explained by classical mechanics.

The concept of entanglement has important implications for quantum computing, cryptography, and communication. For example, entanglement can be used to perform quantum teleportation, which allows information to be transferred instantaneously between two entangled particles, regardless of the distance between them. The ability to perform these types of operations is what makes quantum mechanics so different and powerful compared to classical mechanics.
But why classical object have definite properties? After all they are made out of quantum objects which you said don't have definite properties.
Classical objects appear to have definite properties because their properties are averaged over a large number of underlying quantum particles. In other words, the behavior of classical objects can be described by statistical mechanics, which is a branch of classical physics that uses probability distributions to describe the behavior of large groups of particles.

At the quantum level, however, individual particles do not have definite properties in the same way that classical objects do. The properties of quantum particles, such as position and momentum, are described by wave functions that represent a probability distribution of all the possible states that the particle could be in. When a measurement is made, the wave function collapses to a specific state, and the particle takes on a definite value for the measured property. But until a measurement is made, the particle does not have a definite value for that property.

This is one of the key differences between classical and quantum mechanics: in classical mechanics, objects have definite properties that can be measured independently of each other, whereas in quantum mechanics, particles can be in a state of superposition where they have multiple possible values for a given property, and the properties of entangled particles are correlated in ways that cannot be explained by classical mechanics.