The word at issue was homoousios, of the same substance. Nicaea used it in 325 to say that the Son is not a creature, however exalted, but is what the Father is. Its opponents had two respectable objections: it is not in scripture, and it had been rejected in an earlier controversy at Antioch because it seemed to collapse Father and Son into one thing. A middle party proposed homoiousios, of like substance, differing by a single letter.
Athanasius would not take the compromise, and his reason is set out in the treatise On the Incarnation, written before the controversy hardened. If salvation consists in humanity being taken into the divine life, then only God can accomplish it, and a Son who is merely the highest of creatures cannot. His formula is that the Word became man so that we might become god, and everything else follows from it. A likeness of substance would leave the creature to be saved by another creature.
The argument had to be made against the current for most of his life. After Constantine's death the imperial court repeatedly supported his opponents, councils in the 350s produced formulas he could not accept, and Jerome later wrote that the world groaned to find itself Arian.
His later Orations Against the Arians are the sustained technical defence, working verse by verse through the passages his opponents used, and they set the terms in which the Trinitarian settlement of 381 was eventually reached, a settlement he did not live to see.