I can't think of any Pokemon these would fit off the top of my head, but a couple suggestions.
No matter how hard I crush my enemies,
They always seem to walk away unharmed.
When I am with the older ones,
My only friend outshines me.
Sometimes I get so mad at myself.
Am I destined for this life?
The first couple lines could refer not to strong moves coupled with bad offences, but to a crushing or squeezing move, like Stomp or Wrap like others suggested. It could refer in particular to a low powered one or one that's weak in certain conditions, like Wring Out for example.
The last four lines could refer to a Pokemon who's ok, but not fantastic. But then when compared to a similar Pokemon who's at a higher evolutionary stage(or same stage, but required a higher level to evolve), it seems bad in comparison.
I would say Octillery, because of Mantine, but I think someone's already guessed him so Eevee, because it can learn Stomp (I think?) and can hold it's own pretty well, but when compared to its evolutions (When I am with the older ones) it's kinda terrible.