Why does nature “abhor” a change in flux? I am talking about this particular statement by Lenz who made the Lenz law for finding directions of induced EMI - "Nature abhors a change in flux".
 A: Lenz's Law is actually just the sign component of a more complex rule known as Faraday's Law of Induction (i.e. it says that the proportionality constant in Faraday's Law is negative). Because it is negative, changes in flux are opposed by any newly induced magnetic fields - meaning (among other things) that weakening fields get propped up and strengthening fields get held back.
However, the question of why this happens has many explanations that all boil down to "just because." Nature "abhors" many kinds of changes. Inertia is a great example of nature "abhorring" a change in velocity. Something similar is happening here.
Experimental evidence suggests that (with an adequate accounting) energy, momentum, and angular momentum are conserved. The electric and magnetic fields carry energy and momentum; therefore, do a few calculations and the sign must be negative to maintain their conservation.
Moreover, we believe that Special Relativity is true which leads to the conclusion that the electric and magnetic fields transform into one another as an antisymmetric rank-2 tensor. Therefore, the Maxwell-Faraday equation (another, equivalent statement of Faraday's Law and one of Maxwell's Equations) must contain a negative sign to keep everything copacetic.
Our knowledge of the natural world is a complex nest of interlocking ideas. Change a small piece and you will call into question many other parts.
A: Lenz' law states that the direction of the current induced in a conductor by a changing magnetic field (as per Faraday’s law of electromagnetic
induction) is such that the magnetic field created by the induced current opposes the initial changing magnetic field which produced it.
This  is consistent with the Principle of Conservation of Energy.
Think of it not as "nature abhors a change in flux" but that "nature behaves in such a way so that energy is conserved".
Note that conservation of energy implies that some forms of energy are transformed into other forms (in mechanical systems it said sometimes that energy is not conserved, but it is actually changed into heat and sound etc. so that overall energy is conserved).
A: It's a handy way of remembering a property of magnetic behaviour which is a bit like Newton's first law. Magnetic flux does not decay away, nor grow, just on its own. It stays constant unless there is something else involved.
To change a magnetic flux, there must be something causing it to change, a bit like to change a velocity you need a force. So this also means that if you try to cause a magnetic field to either increase or decrease, it will say "no, I don't want to change; you are going to have to make me. You will have to provide an electric field around a loop, or something like that."
