EFT unitarity violation Standard Model Effective Field Theory is said to not be a complete model because the presence of nonzero anomalous, say, Quartic Gauge Couplings would violate tree-level unitarity at sufficiently high energy, i.e. if you don't constrain the energy considered
Can someone explain why exactly? is the unitarity a strict requirement? if so, where does it come from?
 A: There are no couplings in the Standard Model that violate tree-level unitarity at any energy. The reason we know the Standard Model is incomplete is experimental, not theoretical: it does not contain gravity, or dark matter.
In the Standard Model without the Higgs, there are couplings that violate tree-level unitarity; removing them is one reason why the Higgs field is introduced.
Unitarity is the requirement that the time evolution operator is a unitary operator. This is necessary so that the norm of states in Hilbert space is preserved in time. This is equivalent to requiring that probability is conserved. We normalize the state at some initial time so the probability that we will get a possible outcome of an experiment is equal to $1$ (ie: there is probability $1$ that something happens). Unitarity guarantees that this probability remains $1$ when evolving the state in time. If unitarity was violated, quantum mechanics would not predict well-defined probabilities for events to occur, and so would be useless for making predictions.
Note, there are some cases like particle decay where you can model some incomplete part of a system as evolving in a way that is not unitary. But, at a fundamental level, if you account for all relevant degrees of freedom, the time evolution must be unitary.
You can read more about unitarity here: https://en.wikipedia.org/wiki/Unitarity_(physics)
A: 
is the unitarity a strict requirement? if so, where does it come from?

Unitarity  comes from the postulates of quantum mechanics, the wavefunction postulate.

Since the probability must be = 1 for finding the particle somewhere, the wavefunction must be normalized. That is, the sum of the probabilities for all of space must be equal to one. This is expressed by the integral


This extended into the operator language of quantum field theory leads to the axiomatic imposition of unitarity .
