"If humans evolved, then so did language."
Exactly.
"Because all available evidence indicates that language did not evolve, then humans probably did not evolve."
All available evidence is written. By the time a language develops a written form, it must, by definition, be pretty complex. Can you go back in time a few 10's of thousands of years, and study the languages/communications of the time?
Incidentally, ever studied any cave drawings? They sure seem like a primitive precursor to written language to me. Doesn't that show an evolution of language skills?
No. See Saussure's prediction that laryngeals existed (in some Indo-European language) based on the sounds of present day European languages and the theory of language evolution. "His hypothesis was confirmed after Hittite was discovered. J. Kurylowicz in 1927 pointed out that the Hittite consonants transcribed with corresponded in some cognates to those which Saussure had suggested purely on the basis of phonological analysis of morphological patterns. " [ibid]