I know that essential to Aristotle's existence of matter and form is the existence of change and that the best contender for his view was Parmenides. But I wonder which are some other arguments against the existence of change.
Parmenides's is certainly the best because it is based on solid principles like that of non-contradiction* and that something cannot come from nothing†.
*It is impossible that the same thing be and not be at the same time and in the same respect. †Ex nihilo nihil fit.
Parmenides has two arguments [against the reality of motion/change/becoming].
The first runs thus:151
If a thing arrives at existence it comes either from being or from nothing.
Now it cannot come from being (statue from existing statue). Still less can it come from nothing.
Therefore all becoming is impossible.
This argument is based on the principle of contradiction or identity, which Parmenides thus formulates: Being is, non-being is not; you will never get beyond this thought.
151. Ex ente non fit ens, quia jam est ens, et ex nihilo nihil fit, ergo ipsum fieri est impossibile.
Parmenides's second argument:
Multiplicity of beings, he argues again from the same principle, is likewise impossible.
Being, he says, cannot be limited, diversified, and multiplied by its own homogeneous self, but only by something else.
Now that which is other than being is non-being, and non-being is not, is nothing.
Being remains eternally what it is, absolutely one, identical with itself, immutable. Limited, finite beings are simply an illusion.
Thus Parmenides ends in a monism absolutely static which absorbs the world in God.
see also: The Essence & Topicality of Thomism by Réginald Garrigou-Lagrange, O.P.