The article explains, albeit it's maybe not very obvious if you aren't acquanited with metrology.
> So in 2014, at the quadrennial General Conference on Weights and Measures (yep, that's a thing), the scientific community resolved to redefine the kilogram based on Planck's constant, a value from quantum mechanics that describes the packets energy comes in. If physicists could get a good enough measure of Planck's constant, the committee would calculate a kilogram from that value.
> “But it's a very difficult constant to measure,” Pratt said. He would know: He and his colleagues at NIST have spent much of the past few years trying to come up with a number accurate and precise enough to please the finicky physics community.
Basically, it was hard to measure Planck's constant precisely enough to be as precise as the old standard. For compatibility reasons, the way this usually works is that they will measure Planck's constant and then define the kilogram so that `(k * Planck's constant) = (old mass of the kilogram)`, where `k` is whatever constant that makes this work out. To do this properly, you need to be able to measure Planck's constant with the same level of precision (and accuracy) as the old mass of the kilogram was known. Apparently this wasn't easy, presumably because Planck's constant is very small.