Genes can duplicate and then diverge in function. These are called paralogs. Bioinformaticists trace their common descent by the pattern of sequence divergence. Many proteins are sequentially homologous without being functionally similar.
If 'convergent evolution' is true, then 'evolution' can produce similar genes without 'common descent' and 'common descent' has been falsified.
You are confusing sequence convergence with functional convergence. Evolution predicts the latter will occur without the former. Evolution's prediction is borne out by bioinformatic analysis.
Thanks for the education. Don't be a stranger here... :o)
Paralogs are assumed and 'tracing' their 'common descent' is also assumed.
Evolution doesn't predict anything, yet explains everything.
It is unfalsifiable.